Class 8th Mathematics AP Board Solution
Exercise 5.1- Smita works in office for 6 hours and Kajal works for 8 hours in her office.…
- One pot contains 8 litre of milk while other contains 750 milliliter. Find the…
- speed of a cycle is 15km/h and speed of the scooter is 30km/h. Find the ratio…
- If the compound ratio of 5:8 and 3:7 is 45:x. Find the value of x.…
- If the compound ratio of 7:5 and 8:x is 84:60. Find x.
- The compound ratio of 3:4 and the inverse ratio of 4:5 is 45:x. Find x.…
- In a primary school there shall be 3 teachers to 60 students. If there are 400…
- In the given figure, ABC is a triangle. Write all possible ratios by taking…
- If 9 out of 24 students scored below 75% marks in a test. Find the ratio of…
- Find the ratio of number of vowels in the word’ MISSISSIPPI’ to the number of…
- Rajendra and Rehana own a business. Rehana receives 25% of the profit in each…
- In triangle ABC, AB = 2.2 cm, BC = 1.5 cm and AC = 2.3 cm. In triangle XYZ, XY…
- Madhuri went to a super market. The price changes are as follows. The price of…
- Find the decrease in enrolment. There were 2075 members enrolled in the club…
- How many members are enrolled during this year? There were 2075 members…
- A farmer obtained a yielding of 1720 bags of cotton last year. This year she…
- Points P and Q are both in the line segment AB and on the same side of its…
Exercise 5.2- In the year 2012, it was estimated that there were 36.4 crore Internet users…
- A owner increases the rent of his house by 5% at the end of each year. If…
- On Monday, the value of a company’s shares was Rs. 7.50. The price increased by…
- With most of the Xerox machines, you can reduce or enlarge your original by…
- The printed price of a book is Rs. 150. And discount is 15%. Find the actual…
- The marked price of an gift item is Rs. 176 and sold it for Rs. 165. Find the…
- A shop keeper purchased 200 bulbs for Rs. 10 each. However 5 bulbs were fused…
- Complete the following table with appropriate entries (Wherever possible)…
- A table was sold for Rs. 2,142 at a gain of 5%. At what price should it be sold…
- Gopi sold a watch to Ibrahim at 12% gain and Ibrahim sold it to John at a loss…
- Madhu and Kavitha purchased a new house for Rs. 3,20,000. Due to some economic…
- A pre-owned car show-room owner bought a second-hand car for Rs. 1,50,000. He…
- Lalitha took a parcel from a hotel to celebrate her birthday with her friends.…
- If VAT is included in the price, find the original price of each of the…
- Find the buying price of each of the following items when a sales tax of 5% is…
- A Super-Bazar prices an item in rupees and paise so that when 4% sales tax is…
Exercise 5.3- Sudhakar borrows Rs. 15000 from a bank to renovate his house. He borrows the…
- A TV was bought at a price of Rs. 21000. After 1 year the value of the TV was…
- Find the amount and the compound interest on Rs. 8000 at 5% per annum, for 2…
- Find the amount and the compound interest on Rs. 6500 for 2 years, compounded…
- Prathibha borrows Rs. 47000 from a finance company to buy her first car. The…
- The population of Hyderabad was 68,09,000 in the year 2011. If it increases at…
- Find Compound interest paid when a sum of Rs. 10000 is invested for 1 year and 3…
- Arif took a loan of Rs. 80,000 from a bank. If the rate of interest is 10% per…
- I borrowed Rs. 12000 from Prasad at 6% per annum simple interest for 2 years.…
- In a laboratory the count of bacteria in a certain experiment was increasing at…
- Kamala borrowed Rs. 26400 from a bank to buy a scooter at a rate of 15% per…
- Bharathi borrows an amount of Rs. 12500 at 12% per annum for 3 years at a…
- Machinery worth Rs. 10000 depreciated by 5%. Find its value after 1 year.…
- Find the population of a city after 2 years which is at present 12 lakh, if the…
- Calculate compound interest on Rs. 1000 over a period of 1 year at 10% per…
- Smita works in office for 6 hours and Kajal works for 8 hours in her office.…
- One pot contains 8 litre of milk while other contains 750 milliliter. Find the…
- speed of a cycle is 15km/h and speed of the scooter is 30km/h. Find the ratio…
- If the compound ratio of 5:8 and 3:7 is 45:x. Find the value of x.…
- If the compound ratio of 7:5 and 8:x is 84:60. Find x.
- The compound ratio of 3:4 and the inverse ratio of 4:5 is 45:x. Find x.…
- In a primary school there shall be 3 teachers to 60 students. If there are 400…
- In the given figure, ABC is a triangle. Write all possible ratios by taking…
- If 9 out of 24 students scored below 75% marks in a test. Find the ratio of…
- Find the ratio of number of vowels in the word’ MISSISSIPPI’ to the number of…
- Rajendra and Rehana own a business. Rehana receives 25% of the profit in each…
- In triangle ABC, AB = 2.2 cm, BC = 1.5 cm and AC = 2.3 cm. In triangle XYZ, XY…
- Madhuri went to a super market. The price changes are as follows. The price of…
- Find the decrease in enrolment. There were 2075 members enrolled in the club…
- How many members are enrolled during this year? There were 2075 members…
- A farmer obtained a yielding of 1720 bags of cotton last year. This year she…
- Points P and Q are both in the line segment AB and on the same side of its…
- In the year 2012, it was estimated that there were 36.4 crore Internet users…
- A owner increases the rent of his house by 5% at the end of each year. If…
- On Monday, the value of a company’s shares was Rs. 7.50. The price increased by…
- With most of the Xerox machines, you can reduce or enlarge your original by…
- The printed price of a book is Rs. 150. And discount is 15%. Find the actual…
- The marked price of an gift item is Rs. 176 and sold it for Rs. 165. Find the…
- A shop keeper purchased 200 bulbs for Rs. 10 each. However 5 bulbs were fused…
- Complete the following table with appropriate entries (Wherever possible)…
- A table was sold for Rs. 2,142 at a gain of 5%. At what price should it be sold…
- Gopi sold a watch to Ibrahim at 12% gain and Ibrahim sold it to John at a loss…
- Madhu and Kavitha purchased a new house for Rs. 3,20,000. Due to some economic…
- A pre-owned car show-room owner bought a second-hand car for Rs. 1,50,000. He…
- Lalitha took a parcel from a hotel to celebrate her birthday with her friends.…
- If VAT is included in the price, find the original price of each of the…
- Find the buying price of each of the following items when a sales tax of 5% is…
- A Super-Bazar prices an item in rupees and paise so that when 4% sales tax is…
- Sudhakar borrows Rs. 15000 from a bank to renovate his house. He borrows the…
- A TV was bought at a price of Rs. 21000. After 1 year the value of the TV was…
- Find the amount and the compound interest on Rs. 8000 at 5% per annum, for 2…
- Find the amount and the compound interest on Rs. 6500 for 2 years, compounded…
- Prathibha borrows Rs. 47000 from a finance company to buy her first car. The…
- The population of Hyderabad was 68,09,000 in the year 2011. If it increases at…
- Find Compound interest paid when a sum of Rs. 10000 is invested for 1 year and 3…
- Arif took a loan of Rs. 80,000 from a bank. If the rate of interest is 10% per…
- I borrowed Rs. 12000 from Prasad at 6% per annum simple interest for 2 years.…
- In a laboratory the count of bacteria in a certain experiment was increasing at…
- Kamala borrowed Rs. 26400 from a bank to buy a scooter at a rate of 15% per…
- Bharathi borrows an amount of Rs. 12500 at 12% per annum for 3 years at a…
- Machinery worth Rs. 10000 depreciated by 5%. Find its value after 1 year.…
- Find the population of a city after 2 years which is at present 12 lakh, if the…
- Calculate compound interest on Rs. 1000 over a period of 1 year at 10% per…
Exercise 5.1
Question 1.Find the ratio of the following
Smita works in office for 6 hours and Kajal works for 8 hours in her office. Find the ratio of their working hours.
Answer:Number of working hours of smita = 6 hours
Number of working hours of kajal = 8 hours
The formula for finding the ratio of their working hours is as follows
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
∴ The ratio of their working hours is 3:4
Question 2.Find the ratio of the following
One pot contains 8 litre of milk while other contains 750 milliliter.
Answer:One pot of milk = 8 litre
Other pot of milk = 750 milliliter
The formula for finding the ratio is as follows
![](data:image/png;base64,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)
1 litre = 1000 milliliter
∴ 8 litre = 8000 milliliter
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAK0AAAAsCAMAAAAgncgMAAAAAXNSR0IArs4c6QAAAIdQTFRFAAAA///b//+22///2/+2tv///9u2/9uQttv/kNv//7Zm27aQ27ZmkLbbtrZmZrb/Zrbb25Bm25A6ZpDbOpDbtmZmOpC2tmY6tmYAkGY6Oma2ZmY6OmaQkDo6AGa2kDoAZjo6OjqQZjoAOjpmOjoAADqQADpmZgAAOgA6OgAAAABmAAA6AAAA8yyvhgAAAAF0Uk5TAEDm2GYAAAJGSURBVHja7VjRVqNADA2iUGhXFEeL1aWuLq0j+f/v82QGoeDUU0jm2AfuA81Dz+1tJpMbAjBjhjBW/xHrO4qCR8R/i2MRi0YKeX0DsEIFEGyrMNp+XLkjFo0Ugm1JH0UVQlonAClm4IxYNNJqS4CCsnCxPxKxaMSQIh1hnZhzI/IqdEUsGkG5S41IR2bJ6emKWDRyYmOtAHLMmGp/pBGs2z45lZkrYtGIoSGjC9FcCgXOiEUjm1vTenLTdejhilg0cu6AD6Ft68fawUmV9zONrPPu/lAUvSI+h8ciFs0Mbwi2SHhbuGwlOzu5pmcsNdlH16LfkzNVa+eIvKcs7Wk/P7WpmSjpPm4A1lQbH9do/kH8Kj0JC+TWTD1lGBRmljS5jXVGjxuQnYT5apdatVNF1lNLk6aNWhT4BVbBTKIxTaH7/kCtdecTPBpPBIvG5jba7+iog+WLRnSobSb6c6mEFEsThafk9ncrwQitE6txoNYOE/26/XV3gFhXIY3t0ZNtBAruE/u+iQoi4fmH57ylOZc6WSNuLvekcY11FtsaXmnEzVSxtzIuc+vHrHJbiBXVf1uR4zctThp5FFnnKtnB68BIf3HR+EJOyrqfmbppGdB4u7aqZ38TNy1DGl+p7Wy7ey8cv2kZ0HidkiDWbxp3vZ0Li8YTmgoN/tLs1u6zRqsd0nhCcSCLXGbipmVI4wc95sN9pmLS+Elt01gLdbiCG93BvtP4a1/0M3XSvHNM2bQ4aLzcsa8LEb0g4vNi4qbFRTNjRotP1wx4YFJgI6MAAAAASUVORK5CYII=)
![](data:image/png;base64,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)
= 32:3
∴ The ratio is 32:3
Question 3.Find the ratio of the following
speed of a cycle is 15km/h and speed of the scooter is 30km/h.
Answer:Speed of a cycle = 15km/h
Speed of the scooter = 30km/h
The formula for finding the ratio between the speed of cycle and the scooter is as follows
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOMAAAAwCAMAAADU+j3/AAAAAXNSR0IArs4c6QAAAKhQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OjoAOjo6OjpmOjqQOmY6OmaQOma2OpCQOpDbZgAAZgBmZjoAZjo6ZjpmZmY6ZpC2ZpDbZrbbZrb/kDoAkDo6kGYAkGY6kLbbkNvbkNv/tmYAtmY6tmZmtpA6trZmttvbttv/tv//25A625Bm27Zm27aQ29uQ2/+22////7Zm/9uQ/9u2//+2///bN7FyRwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAEkklEQVRoQ+1aiXLTMBCVTA9DWwiYliNJS9u0QOskUCfx//8Ze0grH5lUSTYHM/EMjJC1631aafX0gjGH5zADOjNQWNtreSp/WPsp1n9uk/vYsbrjRu+sPepG+CzaGMv+qcmjMZpiRxjz5NaU/ZOX10FO0lYe53Qt8rMjjJgJYyYXq2Gck9q9xOhSWNjk7mdqOxjj5NIm35sN+17yCO/txZMxRWrdJi1xxZOtM7NJt2/tycskxU2IBknPrVXx/vrSURqR2w7nsLDnT2aEFWSSds0YAdUa5Y3fj9g97b95RhtevrAaXsqB3230PuvxDsD16ToYozhVAhDj5sEm3xAlxUtxDeAPreFaQwCZAS1vnITaWpXNiWb45DgNufND04gYxWlMcFpjplf2WHICEcwyrJTthsfA7+nvuRj5vZuG8vqeh3qM4l0r/Eg/4xRmnuOFuZ9lsMusrTUwyDpGSrRgLMdXsDd54QokHFKA5wZG5z0yNrVhuKo4XklfNVgOckEecT823rvFOgCnc/KoFnmMo9lnWKa0c9x+POWtiE+jEQoM7rfafnTFRAqQ+/Is+/gF3IsfHCb/iIlOZ8wsgwxMM1p3EPoQq0Jhu6YcwuEhDSQKsG0dByig+E65aLquSQo9X/3ZkqP9I9K2ARM930HDxakOgBgvozM4urCwFvYstUe3aDOEQ41qrW+UUHw7f1IPcgR7D08coLCu6wE6/mb+PZgdk6MCKyv7gQ4YjlMo3mPC0x2zJGeJ+njhVn3U4C0M0sYIpwYeHPFPCcQIHmAirUcrNi0/PsCy37lZLo1QGwwQrNrlZPIWp0kpNiCWc+6H8VlojYS0fIhg+hU7Lrl5LYwdXVXWwL3YlDFi1Tae40MtAzbyi6ffXwU2FsAWHLs88iHqOD7nkQ7jcBXYQiyb+gRhHMNRyw+zjIAxXAUkgAFVKXx2pDAsPRVUWEOwDYyVq8Biz4J7/xrM+aYZ3oGMcPyQR8a4Ayq4dK4WGbirDCzYwPGbGIXfk6P/ca0SPFitgeMHjCwrLKmSqeZAwxlxAECBKpDn+Nh6vHdk3l8FND62Gx9YchDkAOpO4PhwG+g5fuKvAmrhvS6L7072fg2koiy+rzxLRxZ3THnlg5ftN/QoyeKcwdXzuLplxLzILxtryeLMlJ+L5A5aRL2q2vf0GtgKygROHQ9c2pNqZ++tcOsP04joI4eoyOIug6isszpe1b5xGssbOMu8Oi5cuqKvOxYqevx5dxwJIGaYiizu1ipLUPBXVfsmJoI/Enm5XLh0RV8njGKFh6DqoyGLV/YjEo+69v1gz39DxJ51CZeu6uuIMVhtgLysL4u3MNa0bziegFjXMUKxq5Bqshc9fiMEbV1Z3O9H3oo+j5XVNk5PY/NIFav96+0aS1dHFm9irF146Pda2Gq+U7h0hVRTHoOVMkYVWRwmvsKUG9o3Vc9LIJ5BHXdcOujr3l70+Pb/plgjkTqyuEGmTLK3o8sV7Xt6DQofKXJeLhcuHUg12otijj6UCyvPkJJkucZ0b970gHHzc7yFL6jL4luI+fCJwwzsxwz8A1Ciw1a7zvE4AAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
∴ The ratio of their working hours is 1:2
Question 4.If the compound ratio of 5:8 and 3:7 is 45:x. Find the value of x.
Answer:The compound ratio of 5:8 and 3:7 = 45:x
Here from the given ratios, a = 5,b = 8,c = 3 and d = 7.Then
![](data:image/png;base64,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)
If a:b and c:d are any ratios, then their compound ratio = ![](data:image/png;base64,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)
So, ac:bd
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFIAAAAiCAMAAAD70H5oAAAAAXNSR0IArs4c6QAAAI1QTFRFAAAAAAAAAAA6ADo6ADpmADqQAGaQAGa2OgAAOgA6OjoAOjo6OmZmOmaQOma2OpC2OpDbZgAAZgA6ZjoAZjo6ZjpmZmaQZpDbZrbbZrb/kDoAkDo6kDqQkGY6kLbbkNv/tmYAtmY6tv//25A625Bm27Zm27aQ29u229vb2////7Zm/9uQ/9u2//+2///b8f+iLgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABk0lEQVRIS+WV21KDQAyGd6sVPBSpVK1btSBgpUDe//FM2AUKQ2CZaS8ccwMzm3z75wAR4t9aLKVc7IfTT+7k4tWiMhA55FWj4jc2BnafIuWuO4lKHgKNNKgRJLnlt0wGHSFxF4mJe6zQ4mNrkbgwyBaVu1zyobyagaSkDAqUz0r5Zq87DdEq0QgFu32D7nPLJ/6s4wvhTYY4g4IIZ4hLLnGthoiGR6K6MZRNR+x8yuevyrEwT7uoUS9Q18Qs1/xQzb4F1DJDYt2+2fFDAcg8BA52b9hC6kNlY5+pcakRoCQKNdY74y5q7tEvfbcO8nyJtzL7TLvEu1+BaQ9bzNm6q4bTEJ2v5cWLlpeb52xNlwsoAilXw8XD9qNNV6FdX+kGUfSDK9b+oGR4x3P8Y01ZvWsgetS9wD96yCs5WnzvzRrTGFBeVhB22GxEVssWbwa12txTDamWHjuIx+lK6iHBfZK73s9BOaIMtojnAq1E6mR9QXtFxEtEjyGtRDY7B2tYqUtddois2o0K650zXsOpufnz578ufSDKCOBHuAAAAABJRU5ErkJggg==)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ X = 168
∴ The Value of X is 168
Question 5.If the compound ratio of 7:5 and 8:x is 84:60. Find x.
Answer:The compound ratio of 7:5 and 8:x = 84:60
Here from the given ratios, a = 7,b = 5,c = 8 and d = X.Then
![](data:image/png;base64,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)
If a:b and c:d are any ratios, then their compound ratio = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFQAAAAgCAMAAAC7Bq8kAAAAAXNSR0IArs4c6QAAAH5QTFRFAAAAAAAAAAA6AABmADpmADqQAGaQAGa2OgAAOgA6OgBmOjo6OmaQOma2OpDbZgAAZjoAZjpmZmaQZpDbZrbbZrb/kDoAkGYAkGY6kNv/tmYAtmY6tmaQtpA6tpBmttv/tv//25A627Zm29u22////7Zm/9uQ/9u2//+2///bc701RwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABVUlEQVRIS+WV21LDIBBAoU0a74k3tNRaoyTA//+gGy6J1FmXzuCDIy/plJPD7rIExv750M+c36A1sDBbv5ElCpJIm/aB7WqFvGZFo8YLUhokCT2g0vF8S0YZAJAs9PslJIhFmiv1kpkeVlvWV1iCpm2UfcGWnJMIkpk2glevvMGSHDte0RWIkjw6t6A/cebW10GHZwkns8JV17TXRXRBYgU0AtS7pJNBrPVH1+DbLXkc0DXoiEwErPjStceTiGVeKPz4hiXSQlVw6aMHjLG89NNg4kaRZ+iEHJxzaqmS26/vfIhjeJ4QT4L2+Ln3HAmkiMcllSoJpA6Hk+/01Kqpw+Fys+OrR6R6uoN+zpAGx4zL9YH1a/91Oh7TpWOfMqTeseBT+tit4f7PTB/YBf8daa3sHkkfPqxKiw15vqR3LLiEixC9hoYzfrXn99QhiI5MnNL98flPXNAeWm/4DWwAAAAASUVORK5CYII=)
So, ac:bd
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAD4AAAAiCAMAAAAwC5qWAAAAAXNSR0IArs4c6QAAAH5QTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOgA6OjoAOjo6OjpmOmaQOma2OpC2OpDbZgAAZgA6ZjoAZjo6ZjpmZpDbZrbbZrb/kDoAkDo6kGY6kGaQkNv/tmYAtmY6tv//25A627Zm29uQ29u229vb2////7Zm/9uQ/9u2//+2///bHUvh/gAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABU0lEQVRIS+WU0VqDMAyF2wnVuQoyxU4H61SE9v1f0CRt5i6UbF65z1zwwcgp56Trr9RFl9daL7YYYb9eDWKUqdE6tY3mCa4eL1Cxv5PFKrpKTXWF/ZubY7kvxS9DQ6hB02Grbx3JwbyFxdxqvZTNR2eHCZf4sJHkOcVo7Pubkx1gdjuo8LCLrn1JsSFQuIfx+UKKH5oW2kvyrHUBE9jSDNEV/i7UaJKcPgrmYw/71sJTdiXp94Y37tVc7aTu//m+o63BSifi+zo0pRtpVGe2S8v9+P40879e/i8J4QhVqtNn/40z66ID5Xg9s8UcNiExPuvFI9ImMyPUVdzk+5mxMBJ9OdDHWA6nfokIFCojEZmHlGHWgao/ITgjkeBEyGRij7eNyCqwmJB4LCcXAD+IL3lnJLL5L9ZREMTWXB2Q2BU0OmYdbnmoZw8nLctIDE1C5AXXJ1saHHviRbqmAAAAAElFTkSuQmCC)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ X = 8
∴ The Value of X is 8
Question 6.The compound ratio of 3:4 and the inverse ratio of 4:5 is 45:x. Find x.
Answer:The compound ratio of 3:4 and the inverse ratio of 4:5 = 45:x
The inverse ratio of 4:5 = 5:4
Here from the given ratios, a = 3,b = 4,c = 5 and d = 4.Then
![](data:image/png;base64,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)
If a:b and c:d are any ratios, then their compound ratio = ![](data:image/png;base64,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)
So, ac:bd
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIUAAAAiCAMAAABGHepYAAAAAXNSR0IArs4c6QAAAJ9QTFRFAAAAAAAAAAA6AABmADqQAGaQAGa2OgAAOgA6OgBmOjoAOjo6OjpmOmZmOmaQOma2OpC2OpDbZgAAZgA6ZjoAZjo6ZjpmZjqQZmY6ZpDbZra2ZrbbZrb/kDoAkDo6kDqQkGY6kGaQkLbbkNv/tmYAtmY6tmZmttv/tv//25A625Bm27Zm29uQ29u229vb2////7Zm/9uQ/9u2//+2///bWsuw3AAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACCUlEQVRYR+1Wi3KCMBBM1Ip9qVXpS9KX2JJaC5T8/7d1L4QOioUIdZhOezMqCLfZ29zBMvYfv1gBteyn7FfuMMzXETseTiXnvLMor08J3MQBs55xPsK96oF3bvbR5PV8plmo5Zg4LGnl5AqH6u5Es6CvilD3IW5fsGT6xFZEWfbDeFCVtXldahbpN0tcDx+qXc6FLQtKjEgDRDwAm4nHlKjBQomhe0o7kri3IEKoKmUBrc0CZbAkhQ55AYwpTvwaLGJn9L4WpEfsAIcll4ES80fdKGmDlEeUNRcxrs1CJ8pemGlBEnCOc4QSxKs0Mimklq3Gjij/iHpRjEIFLagnqDf04vgheAstjBTUHBGy/B51J1XisSgrpqwMXTRq/aAhC9kzba+eEfbmdAOMDgZ1bilFMiEwsEhmOmlFwMzvbzwAqrB+/LoSqCM+Dn4ceD/A2Omnk9ZuyM61xZgfmmMywZ7kw9ezR1H1WiijticK3jCVU47lvqiVHlRItjuXkuTY3xLj0OrvwI/PAjRoyzui50PSA6TNoDcCHufdlzZJwPugNdHPTcahzQLaX9tYUBurWSTbKDkHl1lQG6tZYNEoeRPNWNB6o9UoOc/DANlZzW05GiUXWeAfC3tV2BPj4usl72RhYTW/Z1EnOYdmLKid1dxm0Sg5B2YsqJ3VLHRF6l/rJbf/kPoTDD4B+RIxCKSmcDcAAAAASUVORK5CYII=)
⇒ X = 48
∴ The Value of X is 48
Question 7.In a primary school there shall be 3 teachers to 60 students. If there are 400 students enrolled in the school, how many teachers should be there in the school in the same ratio?
Answer:Number of teachers for 60 students = 3
Number of teachers for 400 students = X
The ratio of students = 60:400
The ratio of teachers = 3:X
The ratio of teachers = The ratio of students
60:400 = 3:X
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒X = 20
∴ There are 20 teachers for 400 students in the school
Question 8.In the given figure, ABC is a triangle. Write all possible ratios by taking measures of sides pair wise.
(Hint: Ratio of AB:BC = 8:6)
![](data:image/jpeg;base64,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)
Answer:In the given triangle, the measurement of the side AB = 8 cm
The measurement of the side BC = 6 cm
The measurement of the side AC = 10 cm
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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
∴ The ratio of AB:BC = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAhCAMAAAAieUHKAAAAAXNSR0IArs4c6QAAAGNQTFRFAAAAAAAAAAA6AABmADo6ADqQOgAAOgA6OjoAOma2ZgA6ZjpmZpDbZrbbZrb/kDoAkDo6kGY6kGaQkLbbkNv/tmYAtv//25A625Bm27Zm27aQ29uQ/7Zm/9uQ/9u2//+2///bBXbt7gAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAbElEQVQoU42PyRKDMAxDZWgDbQlhKwmUJf//ldQ6cAFm0OXNyLLHAo6aTalmrHLSW6ecXlG5fvrobAMvqieDnAM/k/Yn584trovczu/BkEtS6HcthqSjPWfkUlvFVx4kMP6LrO8OLBQM9y60AV1sBE3Mf000AAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
∴ The ratio of AB:AC = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAhCAMAAAAieUHKAAAAAXNSR0IArs4c6QAAAEhQTFRFAAAAAAAAAAA6AABmADqQOgAAOjoAOma2OpDbZjpmZrbbZrb/kDoAkDo6kGaQkNv/tmY6tv//25A629uQ/7Zm/9uQ//+2///bgKnO6QAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAYUlEQVQoU41PWxKAIAjEyiyyTHtw/5sG2NSHNhM/OywLuwCUddhJSJp7xYRecHckeI6RPC6QjFSnQp0DbLaNlXN1SteN+a1/hGLcBI6VTV9k3mXqfoCDDfxF0J5WXsNPuwu7ZwMXrAWDVAAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
∴ The ratio of BC:AC = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAiCAMAAACk7TNkAAAAAXNSR0IArs4c6QAAAFRQTFRFAAAAAAAAAAA6ADo6OgAAOgA6OjoAOma2OpDbZgA6ZpDbZrbbZrb/kDoAkDo6kGY6kLbbkNv/tmYAtmY625A625Bm27Zm27aQ/9uQ/9u2//+2///bXfyARAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAY0lEQVQoU42PSw6AIBBDC+L/gygoyv3v6TAY3WjC2zSZtGkH+MNVQnZAmGZs0rDLl6yH7qMsomAFdjXgbA08KZziXC4ikWt/fZZScZelzsijdK/TifcQYWzoj7QvrBS7d3+UXsLiAzziUZyTAAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
∴ The ratio of BC:AB = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAhCAMAAAAieUHKAAAAAXNSR0IArs4c6QAAAGNQTFRFAAAAAAAAAAA6AABmADo6ADqQOgAAOgA6OjoAOma2ZgA6ZjpmZpDbZrbbZrb/kDoAkDo6kGY6kGaQkLbbkNv/tmYAtv//25A625Bm27Zm27aQ29uQ/7Zm/9uQ/9u2//+2///bBXbt7gAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAZElEQVQoU42OSQ6AIBRDiwOOiCM4y/1PqdSNMTGxm7do/2+Bt8ZUBCXg6g5T0NPdEnJvlMcgIhKYZYUj77FdxCh591fi1t/4M8c6vzAlrdKea+Y8j8I4rVpYvo8ZpA8sMjRffSc4jARN8P2UugAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
∴ The ratio of AC:AB = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAiCAMAAACk7TNkAAAAAXNSR0IArs4c6QAAAEhQTFRFAAAAAAAAAAA6AABmADqQOgAAOjoAOma2OpDbZjpmZrbbZrb/kDoAkDo6kGaQkNv/tmY6tv//25A629uQ/7Zm/9uQ//+2///bgKnO6QAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAYklEQVQoU41PWxKAIAiEyizTTHpw/5sm0tSH40z87ADL7gLQKkLELgLQoowX89zq6DS6Yz8Bh1h63vKZa6pWi6wm9f/gYz72HMYSg5wXPCwLXnNi71aQNxAHjalxd9Onlt8NgU8DF5b3a38AAAAASUVORK5CYII=)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
∴ The ratio of AC:AB = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAiCAMAAACk7TNkAAAAAXNSR0IArs4c6QAAAFRQTFRFAAAAAAAAAAA6ADo6OgAAOgA6OjoAOma2OpDbZgA6ZpDbZrbbZrb/kDoAkDo6kGY6kLbbkNv/tmYAtmY625A625Bm27Zm27aQ/9uQ/9u2//+2///bXfyARAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAZElEQVQoU42OyQ6AIAxEW8RdQRTc+P//tLTqxZA4l6bLTB9ATh4RlQPwg1y8lea1jHYtuzg2EI3jPi5k67OpnwWlJf03PJehQtXRbzPBmjgTT8n1sPx/xuLm2IjrbIUPgmZfRhehIgM86TJtMgAAAABJRU5ErkJggg==)
∴The Possible ratios are ![](data:image/png;base64,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)
Question 9.If 9 out of 24 students scored below 75% marks in a test. Find the ratio of student scored below 75% marks to the student scored 75% and above marks.
Answer:Given that the total number of students = 24
Number of students scored below 75% marks in a test = 9
Number of students scored 75% and above marks in a test = The total number of students - Number of students scored below 75% marks
⇒ 24-9 = 15
![](data:image/png;base64,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![](data:image/png;base64,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)
![](data:image/png;base64,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)
∴The ratio of student scored below 75% marks to the student scored 75% and above marks is ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAiCAMAAACk7TNkAAAAAXNSR0IArs4c6QAAAFRQTFRFAAAAAAAAAAA6ADo6OgAAOgA6OjoAOma2OpDbZgA6ZpDbZrbbZrb/kDoAkDo6kGY6kLbbkNv/tmYAtmY625A625Bm27Zm27aQ/9uQ/9u2//+2///bXfyARAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAY0lEQVQoU42PSw6AIBBDC+L/gygoyv3v6TAY3WjC2zSZtGkH+MNVQnZAmGZs0rDLl6yH7qMsomAFdjXgbA08KZziXC4ikWt/fZZScZelzsijdK/TifcQYWzoj7QvrBS7d3+UXsLiAzziUZyTAAAAAElFTkSuQmCC)
Question 10.Find the ratio of number of vowels in the word’ MISSISSIPPI’ to the number of consonants in the simplest form.
Answer:The number of vowels in the word’ MISSISSIPPI’ = 4(I) = 4
The number of consonants in the word’ MISSISSIPPI’ = (1M,4S,2P) = 7
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACAAAAAsCAMAAAAzZkq9AAAAAXNSR0IArs4c6QAAAEVQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOjqQOpDbZgAAZgA6ZmZmZrb/kDoAkNv/tmYAtv//25A62////7Zm/9uQ//+2///b/cd95AAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAl0lEQVQ4T8WTyxaEIAxDizoM6mgHAf//U327I0XxHLu+pEmNRK+OLXq432sMhLrFABsHAfcdIBCanhAwdoYWwP4iOZzaJwas77DJFEC65OxDuPWrRXh6OR9nv5T6fKQS/NxbkSCcjdgtRzXElHgpo9ewkkS2/EMroZ67j0bq5Nh9sIBTgkWOZ1yVvRYscm5G8c/N/pqnwARCYASplA3ahAAAAABJRU5ErkJggg==)
Or
The number of vowels in the word’ MISSISSIPPI’ = (I) = 1
The number of consonants in the word’ MISSISSIPPI’ = (M,S,P) = 3
![](data:image/png;base64,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)
![](data:image/png;base64,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)
∴ The ratio is 4:7 or 1:3
Question 11.Rajendra and Rehana own a business. Rehana receives 25% of the profit in each month. If Rehana received 2080 in particular month, what is the total profit in that month?
Answer:The % of profit received by rehana in each month = 25%
The amount received by rehana at particular month = 2080
Let the total profit = X
25% of X = 2080
Here % compares every number to 100,
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOoAAAAsCAYAAABrJSTnAAAAAXNSR0IArs4c6QAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAkMSURBVHhe7V29cuo6EF7OpM8D0GKKDG0aeAAmpEmVgoYOyrhJlyEDQ0cDJe5ouDOp0gQmDwANLZMips0D8AJHd1eyjW1Mopifg/FSgrRefasPrVa78kWr1QL+MAKMwGkjcHHa6rF2jAAjQAgwUXkeMAIJQCBRRG02q2I5eYNuxwRr5qBbrENvOIDVqJ3x401t+40amE7DYrEHT8MHmIfaVa+/RK1jwcyVB0Wo94aQXY1iyTuUzavXl6LbeYGr4XRjrPRM3fHqtjvUOFhuPAQSRdRJw4CKBVAf29CajzLN6rVoGBUwDYCxGIh5W5FVTsaSASb0wBZTyC0n0K9VoGJ8BNpVL98FdpfyyiiP+hJxjYoBxZ4tyg5ZdeXFM8H3veQYUXfjmdrVYZwDmIe66Oqn2+4Q42CZuyGQKKLKodbHkHVI1R7NM4+9orBMC14nA8i6WEy6YM6K0LMfYOSS96kuTGS5205NWpz9PnnUfTTPZsZ1EJWXNxhOm0L215AXZYZmE0lWeoW76QDcP5HAqi9J+N3vl6LU/URPQMDjWwkMc4uxdfXTbbfbnOLeB0AgUUSdZ1uZVmg9yeULCIvnt0qIJq+47OLqk/evPjd3+I0F1usEWh6jv0G0kPdIHl+eAVf4zEoJV/zpesVXqz6SNFOBBf1ROH8mYW3ao1WmjLqiuw7GJYht2urqp9vuAPOMRe6IQKKIGjVWd/Ld3eCERp/QWymLV4Ae8YabCItPqA6aoo3kaMpVtgJfY1u4q7R0fZ9pNb7BveBcW567cvt1bLfRPZ/aAtANr5SuwHZWaJekFpK0lZ0H9sK/tafueHOwBOlB/IBL1Dh+qxO33z8CiSZqs4quIbKxPo52LYNw4epWDH7TRjfXHvdEDfekuAbLFesZg0k9Ozpg85O8KPP4yWrgymoPyR2uAJHUHtzgqh3ece7LyJvjjZas225ferGcOAgklqhuYARZhXvWYMRXFwhFdBNIRssJHMkAk5FB8gtcZePJ3XBhfSurQcs8RqAVSfcjX3e83C65CCSSqF70soCuY+gYZbspbPigrWxd7T1dGTMizUMOv1M9cw9D6L1gxLjTl64qoMsY/QnKO70psDneZI7j9JD9Fxolkqh0TGMiSaNcR3I1rwvoxlofYEcgWrzCJW1F7mY00cL9R9rytpsvcCxi56FLxy3kBrtR5R0srzte3XY7qMJdD4hA4ogqXdN3XAWna9exiQGg0ucjuOeehtyMho9sXmkfiguqGwp29mZOcGnDDfUFXfTkRVspQNKpOi4aTMcCMOJrNPL4Z+McAe1gZF39dNvtoAp3PRACiSKqGzwKnI/ieSitsHD16EGUe3iCuokBG8d9VRFPbINu7iNGhzGYC7TCVO+LwjRNqPXzMGwqwqioLzW99faQOvKi7BNFUmrXbs8zA+GQFSjyq2vdBXxGeOK6+um209WG2x0PgUQRddI15YnpDIM9+FFR2meZskMc9D6SCDYSgVzMjKl+r1MAZ50AQd+NVmWM+hYwhRDbqWbimVISMVNp5SRVeMTSkLdhtiW614XN565l9gRgQkPV+ZMI93fT/V4wDVKNEjALC8deLIr6/TrNUXe8uu2ON/34SboIJIqoMuFhW1XeahQYM2UtZcstaJXdr1e0Qm7gQplIZWxX9trRFjYoSxJLU57/AbIPrpZRz1UyV9//jqs+ZMtQxkH41FOPiDneOOPQnUzc7nAIJIqoh4OBJTMCp43AhQzOmOsUPDw/lOeSFKDJUAY8fegIwwmEnPZwWLtzQCDNVVJkP8VJPN7/nFLByZ9Wuy0u3H2agaTEihEveYCydmRyOgY7+HD+HKZ/csaQxiop1zoqYEoLZzCNTrq+uZtH6BUtMM0uPDnlYqoDllUJzqBJzhQ/I01TVCXlkdQp1CjU6zCzFgFjSqLKfNRhT7zgeltp3IEYqHrOArrBUeVZZzQdeCgniEDaqqRcE0waWE2FXu003wXL2XW6v3nBJIpADrG20zA70MBfF5j5U95TrusJzgVWKWEInHuVlEzawUSe4QATciabxglEfb0DcUu5vPMYlR3XX8/CjUF9Pxd0q1QSNqNSou4x7XzuVVKq7PEd7u2BykO/3qw9Dh3POGl1Mws6fUzJizHpvj3rDMnDe460n4CJDVsLp7WFcEMtBPAK2R9rZA9l57CC514l5Y6PXN5s6D4vwsLul/52r6fBWwiX/Rq83I9hXMD7hXyBJS3rHriRzuQ5sAos/sgIpKJKSl6Pg8DODMq6c2qiFdBmPoP3flG9tVgTVboXtQI8YbL7zbIHRUsFlvTzUJXwY7pER543/DgfAsewcxqqpOgYNHwJvsphWHjnqHhVj5Cur/vPVXhSUV4qAlOBJbqm5HcF1MdyiZg1/xaBQ9uZq6SC9pVEJZdXXq3pVJbQd15gqdKAsY0Xc0X4z/92qvDTzxWBtFdJLT+DZ6hk54vL92chEyHQQ671b70AEp3pqKMcvEXPwGXYnorwJdfnOlGOMa7q5Zd4u928OPwYzz71Z6StSspvD+X2qpReM18i9/ev2Wz+uViVsSLFDe/6KjLCrs1vIrSnPhH2oZ9uPqp7L1PwQlPnErXbfWhyfjLSViXlt2B4z7r6rw1UMMbVMzHnuW4+qiveLXbwP47//GKCn8JuTNRdjK6Tj7qLfO7LCDgIMFFjTgXdfNSY4rkbIxBAgIm6xwkRzkfdo2gWlXIEmKh7mgA/5aMuOg1YzCwhg0pbXhW5J1VYzBkiwETdg1G/zUfN3cJ98QU+nh6xKD+bmeIb3OgVkCYfee0B+fSIYKLuaOuf8lGp1pduTsOXUMkn0eVibu3vy9syVuHDjipz9wQiwETd0Wjf5aNuFZ3LA70s0vrAFyhr3+m7o6LcPdEIMFF3MJ9OPiolr3eukJD+d+QsP4GSxNav19hBCe6aCgSYqDHNrJuPSuJnZg2LglUKZtPZo87wtcpjfDnVXL8kN6am3O0cEGCixrSibj7qzeMY6ouOuuGebuKn12Xgrf3j4QPfRxUT+zR2Y6LGtLpuPqq6mb6MN/b778tYAVYjxXwyd0sjAkzUNFqdx5w4BJioiTMZK5xGBP4HYhumHc9sdqsAAAAASUVORK5CYII=)
X = 8320
∴ The total profit in that month is Rs. 8320
Question 12.In triangle ABC, AB = 2.2 cm, BC = 1.5 cm and AC = 2.3 cm. In triangle XYZ, XY = 4.4 cm, YZ = 3 cm and XZ = 4.6 cm. Find the ratio AB:XY, BC:YZ, AC:XZ. Are the lengths of corresponding sides of ΔABC and ΔXYZ are in proportion?
[Hint: Any two triangles are said to be in proportion, if their corresponding sides are in the same ratio]
Answer:Given that,
In triangle ABC,
AB = 2.2 cm
BC = 1.5 cm
AC = 2.3 cm
In triangle XYZ,
XY = 4.4 cm
YZ = 3 cm
XZ = 4.6 cm
To Find the ratio AB:XY,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAXYAAAAwCAYAAAAFKFGgAAAAAXNSR0IArs4c6QAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAB/0SURBVHhe7V1NbBtHln7Vk3tyjnIkGcTScWSsKO1xpZAdwBpgpcHqIg5gUdrLkMxEe4g01K93gZFh/cxFbAWIfZEw0gBxAFG05xqRAUY5BIhiQyTntrpHAea2qt7vVXeTTYp/Ekn/KN2AE5usrnr1uvmq6quvvvfO0tISeZfnAc8Dngc8D9weD7xze7ri9cTzgOcBzwOeB9gDXmD33gPPA/DAxLvPTX88h78FaaOQpYvdZdEpx3Sz7nZtnHjvuQzEcsLkfuezFPeTtrS8bLZbr/v+ZHJCbs5ERDyVVR8HN/KUi/u1paX67cBnMpCAXWaQ1vPHsEtoyx22q90+JvvPpaYbsJEompZkhEXHfXdTG73AflPPefe98R4oB9RGpkbpyEzR7jIJ86jPFOHTjvdr92Kka3W3a+zuTyOazPRJLXTasYHsSlAfCoh47yE+DmuFzcHLiElN24LPNJmGXXp37GrmNydoTx3WD9jLJz2wMaqCe7P6rvM9D4Rb7DPzEZ0dx8gvyoNa6busSVdH3yAFp+bocSrszdiv43Cv7NvogfIM3Ar0fSqQh6hImelJChtvY59uZnNy4j05GPiLGD/rzsy8plXFIzrImRT9PERGijCAjmjDtEfDrq09tmsIdo2dHVPsDZyZN/S2/w7WOh2N60SZPxEvHk3zgNLFGK+iStfy8q6WPE7LF5oujPuHZBphtUrggJ/Zigg9rlOA0l5gv9lPxLvrbfFAcONJTVgFPxCRTM2bUePp29KV9u0s/kjfYpo33n5NrddQ+JEY4OptdIddZqz1Wrtekmfji4sYfb5boaXvut5cRQOZr3Zoan2dThOf0kG6SAlE9kqKi5/uBHGLazxRAT85J6MJBPwf815gf7WPzGvtVXqAIZAR2q3b5PLyiehZ6qGT5eWqMkXqP39uhg0OSYwJF2jkYrdiWpaceNecnoyTVSRIUQwgPVVlWulro3qSd4HhhoDhoqLokaTZ/AxNxg0VKIPRI8rxbG1pSa3I1YxtelKswiDLatcV3KAv+vZJhKxv4gHVFblAgKEkptHPpu3CRTqanpQ66uBKW8HCebY9PRkTtqsoiLbmH8coBKweS6LLIRuDNnRNtXlehUXDz1JbYIyf7dIojjLoLaXlNuz6z5JdmenfyUUja9m1bmP0LswdfpQzkYRIAaJQz2P9MRmM49fB5ZMT/XIz8kAksladfE8wChhjO0z+ZzOk6SnMmK9i55XtED0/R4TlglWXU85QkEkQgdqyp9k+QTLZL2e0qBi91OnOwaeUOEhTPhaT/mSy6b0lE3oDXmBv5cfnlfkleSBH+5NrNP8EP/gUwzV+CscnabyQNZ0NVQ7Gg/449R0VaOlkV0z0v2tOhrFePjLNnpPWN12b1bP8d2C4hU3AJzFxujpD6ScpysVSWmFr8DIQCwsEe7nAG3bYhHzGdhpRtQGaQ1AtbE2jjCGmMCDwpt75yIVp2lj6umuT9GRlmUJ3OZjmxH7E6rdU/Q6QHo+gvmMZ9ydrBkgLQomJ3sM84HO/ZhYzl5sRXYQDLzgwy3AopR2n6ZIxaAer7kGgdc+AT3qApR9ZWPq6C4r5bmWFwv2msusg8hCDxTew6x+UmYFdiQit67DLDnYcRIcCCdhxpuwoZDYvI/qHIhq4lAsoUx3c1WYuMOwEY9jyGBh2kTZRb+IH9AMgHYW2NZn/6JLrdL/51e2YVLzcmgEWjkJ9roLuchL2FG17pmFPqkmALm6ukgGcPCXQj7GBy0TipSigbhcaU/PHmJwALg9bjH+5T4epkBfYf0khy+trax7om0/RCVgxJyieHI2aZBj0Ar+uHvv2zFqccpiZPgn5aBeFfCGdxoNxij/NEBYALV/XqadvfttirCCI+yZ+SwMAYU/zRfWTV4FqcFFQdJRn42oW70v+hqYwuzeePkOZMP40P6/CbYR9zIrZNZOjU5J2DMH9rhdVMmsxyk2lKatbDBese7Tk4w15gGD/dWabdDTbCXpN3xzsAvau7LoHuwxDvIRdAtGOe6X8OLBOX2KZgPUHArNOY8EEJb7OkDLiStcL9BKLl4FHwKOF3d/P1uVBpDFYXm7Hp9pR8AfsicMe90PP/Mmxx6c+tt6PBMVhjxEO130S1sboopjCfoTqhz5OwUSC2Je47epl6EQGr7yIFhbw3+A6pbFa+udfxa88VkzLP0Ov4C/DA0G6g4BxwVGdL7U5Vr6wVDan8TMObujYCLRm54zX9/chhp3maSKVNJ3PG/mrlXoQFjQqbl2txhdQM8RW+DvBOz5AMxxeq+Gm6mrRb58rPvl7K/pdXZohg2lNiIF1fyX04/PDNkE/FDDocOQ9avetCdJHqKbUg6rNSgu6gB2lIK0olFp/L2b7p3mRl2HpF5UwBiA47d7UgDQSARE8iMpfP/4M0devDQ8vm3tYKfCFWXeF4ZXtuGiNDe0pldP679j2mKH6sEoxTfvEA5TdtK/JgBBNE6Vcm6eYsesfHtCjs+NLL7C3+9559/8iPQAeNge0qgnpC+IJ7nWuRvXw8ruVGS/PHO/2IXAYq2IjbwI6IW0CuPkObp4KcGB/lZefPsJImGo01e+COblEgChhzV7L10s8DxMLjqusFYaA8oCAIg8MoQdAjQpGZfoYM2MXtbAdM7+taY/1ftSDVYrpfcrlchTQ4tw0YCj7yj6l9HZIhhvAOGr1sJ2W0R1dfBrZ9KCYdh6ed+8v1wO1NlTZG1c3Yhv7qFE9CkGYeK8lJ3+cKtDGaaC0MernDUTsAahDMw0OArVU+bUKWTBHcKxqJn+tOq5fuNaGKtfCWH09UssumC/D4F0+nntXRvSE0GfuAdoAVNIctWpq4ECNDd5G9lgrgr9hn0FWUD6T/f+L/YcvxNNMqjYcU2EJ2DID+CD7wgvsTZ+QV8DzQPWPBzNSAzPSkWvg6VedaFHW2q/Hqrm4NUn749j8y/nKgfxktyNBqvYLYNu/f0R5CdaGA3cUC4CITOrzY6XAyw3A3N29rBWC4QbdmzSoNjeBp3/5DR/+IWabaHNTptQB3ZxJQCXoCxU3q2qx+1vdTuGFgrrKdE5XuaZbnq4mMl+RERyjMwuWL1+h34Aj9AX2SjK00wCft24o0Itv8b/gHS+wd/el82p/kzxQeGGBEmrPse6Vq9goJfXDLbMeFP99PmrG8SM7PyqABYN/JyfM4uYardFsE8pjue6W67G5527WBRXzFfh6afN0vAlw4+ulAWHQPmbyvBN7N3ouz2ZTggpMd4RtRdyPSGfFiMb8c7X0n5uSCT0uIlthlgggs8AUQl1kBzaAEwtrA7CVS+H5bFeR4jE/HZ2fy/zsNuxiumOOKmJpVSAt26GLaDoPllBSY7ZKcfOheEh/oFSsDuUxl6CHmTAm6LAb1EcoHgizLwAYxFrh4ORpRcDmdibGBmQ88UCsp/0yjnYILKCZyN+UpIBzWfbcl3H9EzF170wmAZ9g2L0sbsEe8w+0DXuqKY/OaVLC6dwAoKCaFM0dwDEpC47h0VK9ynfK7Sq6K7NiYMzAmO4F9lbeO6/M2++B/vMF8NK5HznEtEHWgynRF/lT/JAhJ2AdQzXC1vcx2qRBv4XaAtIAtGHRGXF4RRQ2ooriiDvMhYXn4LHP02wMLJkae5S16mbqZLN6rJOiC4rjDco6c9llMtRP0xoCqUX8Zq65FEyN2wQ1LqYI6pIJEs7FfPcnoL/xRizPTP84FZQhRWQPyq9Gs5RCUNfQb6uNIUVvjGHjcCiwoOjZzD+HDkpN2iAf4snjSP2kbrXLe6VBbOjlmQuOmTDz2B0tlYb17P6EGXNQ6mxXPCifpo9pG0Hd4ZIb+hDrxci4smvxil3Yvdby61EZ+QT3m7BD8djn6DMMNmDD19g2DoA1E6R9Hbg8243/BKPrlt08GhWZPrmoArbb7iRNUPplhHTcl4D/FO/9yzE6/TBXKseBnP2cX78Pez7EaMGUTeaxz+H9uIquWxCMFZDNLFgup+vyP47/qGQEEMAvZ/iEKX9HO8RHAdJyVhb+VSf12Q7K77hZMWjn8DH92z+/91gxb3/I8nrQigdOepaEGztFYK24jYOsW8Kav+cSI7hpxCl5Ur5n96JHVHwHGs3uskOlqbSoVt1OiUb1LCPgjeD0Y7n9FeImevBZCQa+2KOseVdOD+ZKnHUHU0/excAQCou1UcVlV7DM37FpuLRk14j+LIPEuehyzMUe2oBxw2hj2DGywelLxqkrbASivbfioNr26c0W6uHNzEXHLrS3Qu+TOvlpXz+X7FqsaRf8qFXY/DPsWK6Nri/vnmg0PEwj/KfcAuwuPV/UdbUdpnPS+8Pwl+MZtLHHvrLLwm6nyd2LDyrrYHtKfim/H8zQeR/3L1bYYTFzcFV9x3sGqkFaLD2cqrf/uz16iY+uxYp5k1XqWvlxv+oyvETfhB5JvMEJxldtk9fe7fNAcWuFdnI4rfmxwEwO/XPi08egRWI66vDdb1/PvR7V88A7b4oCXjcfkbMUxlKarnMysB2bVFAf9FO87wgzpRPBfp5sUGGpPG1QIRsrcaT5ltJ3NXlrfBR6Xi23W+FPN+pT9bvg+MsNJVBwnuZolR44tuCgjmOvxc0Gbqka6bz8bTvP4zbf6wswAm/Q6hb42KwYhYmuIzFgmJAN+D1OpcZcAf82O8Prm/KAPWO/HQp41hHtfT7+3VE97Ru9K3zYAMEvOo/TBidYpjfRLcHxOaXoRjiiwIpu7ktttGWPzBccNIGZLvWcqB0uDviZTSgUxoEN4iTIdU491uoT21iAdK0fmCvT8JxBkKGEoyiZYbRRUHjtJA2qI+x4b56UByHWXkkdRSE4h3MpBev05o185910LQ+w9EA+A6x7pYyx80nEYHQDzyEGbnbnNdavZaBX+JV7QAX2W6OAZzMYqtXrShinCyPtuqer2BTN2ss8NbABt0Gn8TjtQ9GtjP05d9qKbq6KVMBPQqEQgd24xqnHRrb4QrO0ETQoHoduiJkywcsW1oDJuuXlVUFydsMMGpW2OisLnul7Qb3ZE+/s97sI7iMjwOMrXpwLfg4tiAl01havttfvgXeazSRflQKee7nPgWE2P20r2VmriZivCHbRGk2uQt3OhgF4x3/Enr2yGp9YsNXrLMoWa7PREY40h222QzUUU6mshwGOlekwA20WlJrdx30ZLDEsLFsawUAWhBGlUROKbvvQHNlP05Nsa0fTS68QqFrtQjFclxosnmyY+xC5Ck+PQgjLgpT6OFjbR+hVud0LMc+zeNcAoFYdDCVhkcIaKt7lecDzwOvxwLU2T8smdl4Bj2fVZmFDqeadrk7T2vwsPTm6Q5PhfTQL9TUbry5kU4ACbNU9Y7Wkuodd9VKWGndqM6Ag4Nda9bqvamU9yHiam5NhiA294EQMaqZa65G0ch/3JQtIgulzpYDeYLWgFN2Ak/cgqE6MB814vLWj6VB0w+YsKHdBDGCASE7qsDIcm3MuGKfR68ZB+8lGEEkpVokZzqfYJxipoVoYmt0gnrWvbs5SVu0pTAKa4WxEHgTzen7OXqueBywP3DCw48BGNxXwxnHQAwc/WEl7BBSoi138DcvMJSpTyhwowK26d52HqpTaeMaPdqwZ6ElppsrHd+sdKrzpffVss+ALKGPbWLyPFd0Ax9S1AQA2aMrqSISl6AYclVcZHQ6mvtg8KYgHUrAMwdQaNMoDwBoY36e03zdPIzfA1csc82ZP0NuQbeYh73vPA20E9u4q4PVBuAgxvGtXWVnPLeOH5hzVPBxNrBXYb3pfw44oRTeWgLXhC6Xo1kACtnrzlDcxsWFcfeDG3SYHYItzfR2n2ph+DmwLzMivYv5WC84AEI/XHwCaPchqjnmj8tX880ZlMfC1oqHVzDzve88Db50Hbjxjb6WnnVLA47bUse1MmtZW9+kUILtzuq7iqHUrRjUsc1P9jpveB5DJVnTzK7l+PsVoHxvMPaX+BpAQF7bSux0hvVuY4pOboB1eE5dv4Isi2Db740d01Ad4yo2jX7nH2dS9o5QxrjN0tP24mlSAA0ceK6fbTvbqfyM90NXA3ikFPDcnvIBUVozhZu0sNp31KkR0WJluvGom37SRm91nrQCeY7ZtVtAznY3kRpBQ2SRnZl0fl78uxq7KT/bRfDZEoaKFo/NGart0ynpu9KCYpi+YV8DzwLU80KXAfvMZbE3rFcebOdPtH8Kx6neU6arYJ7a4Un0o6Kb31XkmmafY+BynApCnisycoVHweTj7TSsZeaxBhRXdOjFjdgbRvnmLBcMzcGsjlUWvrpf6rdU3sVtQTKvte+U8D9w2D1wJ7K9VAa8e91tlKYH6m83vZgbL9Nrq1WdRVa7//NzMz0LVB0JHtRX64jS5qSv82GHFWCnPatP1yop817uv1kvjBFDwCOuzSAw3HGMHcBf2pA4oMSuG4/p4OaNPdXvXwdgZgqmmLJY2UsPTfPDIbEYHvW0/Eq8/ngfeNg9UBPbXqoCnoJWykh5gHNPJDG9xpoPgTFtZa56fs2LdPK0BW65Q3asoFwR3HOp1rNDn4pRXKPSBksgKfcwyUQQTbEzyycpGdD2lyNfkvko1v7IqoPNyWBCMFZApB5ZLcMOsfSzf4FODYKXMKi65Kn+FFcMJFZ4oFlE7L58z0PjVUYBcacDjf2WmHZkA2OM/LW3UVvQDw4FfNKaKtmNft+/tpg5SN+tu1y8T7z2XgVgOCpJYEbuSXLdbb/X9SloY2rjxVFZ9BVVKlvptmAQEfpOBBGwzg6zuCLUEcUXyttN2Xrc+/NaRCMNQSpBQwUSmujfDxorA/loV8ErMDdu1FxXgBDFPvaRKp2iPULkD00Ppv7k44hXlWL0OWEJdhT4E6YrvXHTKRg8YinYN76tW83Pbx/Vah75cCn10wYOJavLqd9w9m+5Zj5qChArtXrwaUZRSpw2X/+u9F7VtbZZbs11LW7//TdFB4kOAJqQaRLiVLKWt968TJXd/GtFkpk9qodO2JgaNbFFBfSgg4tAbx3FBSAwPXkbMxomjuT74TZNp2KZ3z7aGdttBe+pQqWPW1Eln6WIJ6WIO7u08j/IgZtUyhUGC26RMFNLHX2DgwMgRnKPP6b/pf6DZrOheSF6dP+ZkIdUSv8Gb89jb6YR3r+eBV+eB26GD1Al/WfrufxHjZ1nWCqud0KETDVXXUTyiAwSj6OchMoCM7i6PaMO0R8hKV7rYtiHYNnZ2XJEarhvmdLzOqoTWN6mfB7F8ulcGEMQHHp0hW5LQPljmxNwfaOn7yO4k0uJM6dxHaGgmQLoxQI8eW0HdTtyhbafvS6Q8FYdn215gv8lD8O55ezxwa3SQOuFyOxtTtZZSJ6puWEeTbEzqXrvMv3fdmNYb4Nm40oRvoEffem3NS/pC/wWdpi8onlijdCxlZUsqbl4OBaLi8DJkp/HbNZOfrcugkRAH2HNMYITm8dHJwnT/8P/on98LL9FGc3d7Jd5WD7wpOkiN/FepO4T9kg3sl1xY+yXJu8BvQ8Bv8XdkT4J+0oytn2TtB+WQVglcfbUqd2R6V6H9f0XdGYSAL/r2SYRsLSUlAsmZd3CoTGIK/YyFI/gq0tH0pNRRB1faCg7OM+3pyZiwUw5YekuYSYawIuCZJGPQQzYGzdmIuN1zG2ZwUsBB50lqC4zzEyUCGrITEbIOQV9eIv/RM06PZ9mWmf6dXDSylm01kkVzLtOZSEKksqoEsig9JoNxfDXzvXqBMIFUfg9EAhRqqwBLYCMrEs+Mn82UMjgxdu6GYirbIXp+jqSr7vx4dlNOOQP28B7GlG1PdWo8xzKVVu/xutwPILE26MUyFZB/jiSQMe8Se21l7B57jtocz+I/XROlASATxS7XOp0hJeH3eLxdojs2epW97zwPvMke6LwOUr3eVusOTfS/qzbzsVtupeCDYqMsbAI+iYnT1RlKQ4cnF0tpha3By0AsLDhV3gJjv8jR+UzJKEfVBmgOQbWwNY0yRimr0vnIhWnaWPq6a5P0BFmDQnc5kObEfgSKnk+yCCgcRLHcj0dUqry4P1kzOFrwSUz0HiKJdtiv4QThJec8DQdecFBW+T45TdyxjUE7WHUPAu2SK7kRZ0+SRxaW/ghQjLNJ+t3KCoX7ObVcThxEHmLA+Aa2/YOQ25P0RITWddhmtWGqBNUIiL2HZ8qWQmbzMqJ/KKKBy5pp/RzcP2E+ojN5jNkw9KhQb+IH9IVAiwttazL/EWbLiQrsvLodzq+6hVyjcdzlPizpLidhT9G2Zxr2pGyba70XHLQfrw9g0/iB4OH2R+xL5PCM2Wfu8qH/wvmSLxL0AKfCQzEh//zgBa1/maLv/yp+9fLlsvQC+5scYzzbXosHuqqD5OqR0h1S9FrkSsUmvy9UX06ib37bwsURxH0Tv6UBiPc7mZFKyayjo0iDyoF+yfQlf0NTcT4L8QwtQiC/BfFebiPsY+wdy/3RKUk7hmAtJnVAosaVWYtRbipNWd1it3DquOTjDXmAYP91Zpt0NOuC0dt6ln1zsA2sGGXbPdhmGMKd5Fr5cmAdSbT9VhJt+HIsmKDE1xmqbUiBXmIBM/BIRwJpu8+AOA4ijTd1y+34VDtqlg174rDH3cHMnxx7cEgFl/VsExSHPQYSoTfyi6IXJ5DXdOc+HcqQenrVlITyAPBQsE7TX3vnKMv+2bMGAC+wt/W6eTffPg90VwfJ8VdZd6h8/oCZSf19WLXb2vqcgJqKW1dd7GgateD84B0foBl3vrx6N6HfPlds8vcCPKh/cRLmaU2IgXVFQS5fPkg8Izb+UCgScXbrjkT2IH2Eqkq9qNqstBJCw5ZSkFbBTevvxWz/NC/yMiz9wprZO4ZyrtF7UwPSSARE8CAqf/0Y2ad8fm14eNncw0qBL8y6KxxQ2Y6LJdPQnlI5rf+ObY8Zkv4Gs3bnACVld9SMXLdx9Oqn4QwAnyauDgBeYG/hx+EV8TxQ7YFO6SA1qocnyq2omPGs8W4fgoaxKjbyJqAT0iaAm+/g5ikI6tXMqNi1R+qnjzAipBpN9bvUdi4RAEjPewfu6yUV4EV/jYk4Q0B5QECRB4bQAzglEozK9DFWBi48ux1Tv61pjyX9UWcRpJpTOk1jh3TY+wl98ml5I/UqNm/LiZjWqXP35QX2dp6cd+8v1gOd0kFqVI+a7E6815KPP04VaOM0wFAMl5d+3jw8KlibfoBJWqqkI4UsiCM4VjWT70jdjSuptaHKdzBW74L0KyrBmRTM0pfo8dy7MqJj03LmnjoEiGMmbV8DNTZ4m9mjsPlIn/j8G0Aw/wCOvhMn3khVNl3DIi+wX8NZXlHPAyWdIcxIR+qJ9rfkps7qKRW3WI0TG385XzmQ4+BaJwJU7e44uklHlJexMtRRLADxNanPj5VCKwhQS75qVshaJRhu0L3JLVYAJfHlN8wFVwwebW4KTBNAN2cSUAmgG0ydq2qx+1zdjpJCMam3VNpVruHcvLJ6h7LY+7nNgtn9ybQ2UnVxf1Q6m9EtDdJeYG/2znjf3xoPvFYdJOXFHDmJYcq6QyyuVgALhvPXQpp6c43WCIlmbMoj2dzzCnlqW6zOeTClzdPxJr95Xy8NCGguYSbPO7F3o+fybDYlWEtJ2VbE/VZayRKvvBysKl8DtWk4NyUTelxEtsIsD4BMZUwf1EV2YAObmMLaXGz17VGYvkEON/vo/FzmZ7dhG9Mdc1QRS6sCadkWXUTTeTCFkhqzVYqbD8VD+gOlYnUoj7kEPcywLAlsB/URigfCRIrJgGatckDVrAjY3M7E2ICMg7GynvbLONpBvs7LmcjflKSAc1n23Jdx/RMxde9MBWQALJfFLdhj/oG2YU8tyqOl0wSWDkg5zlXaSNWnaTSfajm4e4G91RfPK/dWe+C16iAhBy6nSeTLCA+WtHaU7tCGpVeEb6FX9Bw89nmajYElg4honRRdUPxuUNaZyy6ToX6a1hBI+cN4gLnmUgjQ+zYHLhMxhcNIR9Kf22O++xPoH/FGLM9K/zgVlCGF1wTlV6PQUkJQ12Cb1caQojfGsGk4FFhQ1GzmnoPHXZMyyAd48qAyTupWu7xXGoymKa9OSJZ57I6WSsO6dn/CjDkodWxmUiIon6aPaRtBXdNTth1DrBcj48q2xSu2gZ6i5dejMvIJ7jdhi+Kxz9FnGHDAhq8xwATAmgnSvg5cnm1XvsIR/W0cBOIRqcj0yUUVsN12J2mC0i8jpOO+BHyoeO9fjtHphzlVzoSvDJvmmV+/D3s+xGjBlE3msc/h2V5F152ZekDx3XMUgTAhD5QMvWSilk6TSTukB35UPrAGCgwoWkAYMNCEJQGNKaYp+VEy+auXyx7d8a0OVp7xrXvgteogIYCDglgy1p0FaveiSnfoopz+cRnBbgQnH0sSQScrSvuoB5+VarvYo6x5V04P5kqcdQdTT97FwBAKi7VRdcBGwTJ/x4ZhSXOJtZSQK2zRbdse2oClw2hj2LG4wclLxqgrbASavbdSRrRLpzdbqIs3MxcdsSK0uULvkzr5aV8/l2xbrGkbfKlV2P0zbFmuja4jFaZGw8M0wn/KLcB2ixGDC3VdbYcpnfT+MHzmeAdt7LG/7LKw22ly9+KDyjrYHpdvnIZ4ho8KaNGp8uc9GrGXOicfLOH0a/k9d3zA9r2PL1xfqb0E5/Jm7K3HBq+k54E30gPFrRXayeGk5seCDDeu/XGA+jAVdfjub6TxnlFd8YAX2LviVq9SzwOvzgO+ACPwyE27BS42lvA8nXckBgwTsgG/x6nUGIq0DHi/Otu9lrrjAS+wd8evXq2eB16ZB1h6IJ8B1r1Sxtg5d24wuoHEKDHW9H91So6vrNdeQ4084AV27/3wPHALPLCL4D4CPf2RCs3+C0K2q2vxn2+BK7wuwANeYPdeA88Dngc8D9wyD3iB/ZY9UK87ngc8D3ge+H+GIM+Op3lepAAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHYAAAAsCAMAAACHbLyyAAAAAXNSR0IArs4c6QAAAGxQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OmaQOma2OpDbZgAAZjoAZjo6ZjpmZmaQZpDbZrbbZrb/kDoAkGY6kNv/tmYAttv/tv//25A627aQ29u22////7Zm/9uQ/9u2//+2///bGSd2GgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABpElEQVRYR+1XXVfDIAwFdW7qVj+raOfWjv//H6UFWlJHQjE7vsBLT0iaC7eFc68QZfwnA/vHjyi83ldSrnweRviasa7mza6S11/RDkq+im7nC2CEweJdhWjvP5sJ9vRkV9C5p1BrEzXyzULACIGFXc8XBrC6XvW4p91DWHr0sMMkjKLYQVcSVuj69mBQ+z1OQ4GvACMe2B73u1ofwm7txnE8TMIoTvSi3QqDK82Gg6HrbTRCPu8fYXUdMg4j7F9eBjuQHG5XAcZhxAbrf6mR5qZfwtHTDCMMVdC7vRpvqQG1P0Ce2PbO5LTa2qkxQgFtspm6nqnW7xsp5c2LTXXPdputewplkmY42DGiYGFXqrrkCwOFgRgD7tCZU4ge5IUE5nW1t8HSQS1t6kdVXiyfRwe1nMt0pVBLPoUBQuhnugLSPhBCP9MVkPYBCn0uV5BmH0ahz+gKEuzDJPT5XIFxTIilG5RTIPvZXAFpH+ayn8cVwK6/D9VM6M/NSKYrIO0DFPpcroCyD1Doc7kCyj5Aoc/lCkj7AIU+lytItg8p93epIRj4AS3DKUeb5d/mAAAAAElFTkSuQmCC)
∴ The ratio of AB:XY = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAhCAMAAAAieUHKAAAAAXNSR0IArs4c6QAAAE5QTFRFAAAAAAAAAAA6AGaQAGa2OgA6OmZmOma2OpDbZgAAZgA6ZjoAZrb/kLbbkNv/tmYAtmY625A625Bm27Zm29u22////7Zm/9uQ//+2///bgWo6oAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAWUlEQVQoU2NgwACSAiwgMSE2bjDNwCCIn5bkZxYFqWIEAg5M43CIgFQDAdHq4QpFuBkZ2RkYJLh4GYSZ+MDC4qwQWhBivTBQGsSDUGJASoyHQYITZB0PLvsALysCbKWAqqcAAAAASUVORK5CYII=)
To Find the ratio BC:YZ,
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAC4AAAAsCAMAAAAtr3oOAAAAAXNSR0IArs4c6QAAAHJQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOjoAOjpmOmaQOma2OpDbZgAAZjoAZjo6ZpDbZrbbZrb/kDoAkDo6kGY6kLbbkNv/tmYAttv/tv//25A625Bm27Zm27aQ2////7Zm/9uQ/9u2//+2///b3nf1gwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAA6klEQVRIS91Ufw+CIBQE+0VZZkUWZpkg3/8rBrQUdXvA5pyLv3Cc9+4d3ENoLut5h5SUaXPMCVYrAuDiiBePHxsnF7hFHudFAFyRTQjfEbwCjbHFyOsZCQo509FubOHkANljtWpgdbLxhDPN62I3Wg0nU1tB23sYVJGZvvfl6QsXqfqI87k83r/QwXSuzIKfENRsQ9HbBBs0hpjgolP8IF9b7Mq0pYNFN2embbiOZ4EdI6/bJwNSN3BEZAGpqxMV0neIqyUJEYNQhcHx1S/tmEctXFLNW/kaKfXUFXTt26vQw2zviw4xcATsB3EWDNIVUe1gAAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
∴ The ratio of BC:YZ = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAhCAMAAAAieUHKAAAAAXNSR0IArs4c6QAAAE5QTFRFAAAAAAAAAAA6AGaQAGa2OgA6OmZmOma2OpDbZgAAZgA6ZjoAZrb/kLbbkNv/tmYAtmY625A625Bm27Zm29u22////7Zm/9uQ//+2///bgWo6oAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAWUlEQVQoU2NgwACSAiwgMSE2bjDNwCCIn5bkZxYFqWIEAg5M43CIgFQDAdHq4QpFuBkZ2RkYJLh4GYSZ+MDC4qwQWhBivTBQGsSDUGJASoyHQYITZB0PLvsALysCbKWAqqcAAAAASUVORK5CYII=)
To Find the ratio AC:XZ,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
∴ The ratio of AC:XZ = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAhCAMAAAAieUHKAAAAAXNSR0IArs4c6QAAAE5QTFRFAAAAAAAAAAA6AGaQAGa2OgA6OmZmOma2OpDbZgAAZgA6ZjoAZrb/kLbbkNv/tmYAtmY625A625Bm27Zm29u22////7Zm/9uQ//+2///bgWo6oAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAWUlEQVQoU2NgwACSAiwgMSE2bjDNwCCIn5bkZxYFqWIEAg5M43CIgFQDAdHq4QpFuBkZ2RkYJLh4GYSZ+MDC4qwQWhBivTBQGsSDUGJASoyHQYITZB0PLvsALysCbKWAqqcAAAAASUVORK5CYII=)
∴ The ratios of AB:XY, BC:YZ, AC:XZ are
,
, ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAhCAMAAAAieUHKAAAAAXNSR0IArs4c6QAAAE5QTFRFAAAAAAAAAAA6AGaQAGa2OgA6OmZmOma2OpDbZgAAZgA6ZjoAZrb/kLbbkNv/tmYAtmY625A625Bm27Zm29u22////7Zm/9uQ//+2///bgWo6oAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAWUlEQVQoU2NgwACSAiwgMSE2bjDNwCCIn5bkZxYFqWIEAg5M43CIgFQDAdHq4QpFuBkZ2RkYJLh4GYSZ+MDC4qwQWhBivTBQGsSDUGJASoyHQYITZB0PLvsALysCbKWAqqcAAAAASUVORK5CYII=)
Here, the lengths of corresponding sides of ΔABC and ΔXYZ are in proportion because their corresponding sides are in the same ratio
.
Question 13.Madhuri went to a super market. The price changes are as follows. The price of rice reduced by 5% jam and fruits reduced by 8% and oil and dal increased by 10%. Help Madhuri to find the changed prices in the given table.
![](data:image/png;base64,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)
Answer:To find the changed price of Rice,
Original price = Rs. 30
Reduction = 5% of 30
![](data:image/png;base64,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)
= 1.5
Changed Price = Original price – Reduction
= 30-1.5
= Rs. 28.5
∴ The changed price of rice is Rs. 28.5
To find the changed price of Jam,
Original price = Rs. 100
Reduction = 8% of 100
![](data:image/png;base64,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)
= 8
Changed Price = Original price – Reduction
= 100-8
= Rs. 92
∴ The changed price of jam is Rs. 92
To find the changed price of Apples,
Original price = Rs. 280
Reduction = 8% of 280
![](data:image/png;base64,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)
= 22.4
Changed Price = Original price – Reduction
= 280-22.4
= Rs. 257.6
∴ The changed price of apples is Rs. 257.6
To find the changed price of Oil,
Original price = Rs. 120
Increased price = 10% of 120
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGcAAAAsCAMAAABPAFZkAAAAAXNSR0IArs4c6QAAAG9QTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OjqQOmaQOma2OpDbZgAAZjoAZjo6ZjpmZmaQZpDbZrbbZrb/kDoAkGY6kNv/tmYAttv/tv//25A627aQ29u22////7Zm/9uQ/9u2//+2///bxgcFFgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABoElEQVRYR+2W627CMAyFm20MNraya1hY2XrJ+z/j7NhtUxpEJGyhSeRHWxDywfbxVxfF9WhUYP/yFcL6rTGPOw0FjNluzO13kLH3v62lZ/nTrHcVxa5vIK3afMprcETWcSjXlUtlHSwb6uBV51A+pENXnXMJHf3+FOyDZ52iQVT2W4WWVvU1Dg5ZTc8Gfrsyxty9ExnMWs1tau34J4GZ7n4PVV6ExmpwfqC7Mx9FWyJJBDjfvdJbouV7MdLdIW9pFM7nvLcLFOrKp7GpPG3hizBtEpwP8zRlUayDEjHnHYwIHRrJ/ANRfjbLeKginWYF6Zzk/KCdfOj/irdm+qYYdbxFFp7UyUvquI634dXb1w0/nFm3SUJDPo7LKcH53gdRg3qdCtVrqJwA5xnfE8NVZKXmAW7egY4A59s3SqThOyCmpzu3Ap2Qwfn5KqoKqxFRArCa+Ti1igrAKjUvs1VUAlYJoXh1G30jv5QerohCEJlldAkdnMYYVnn8y/vV1AcwdBKwOuqDCFECsEr6+nAVFYDVTCe5imbAKq8l11/lVuAPWpUueCTI9ykAAAAASUVORK5CYII=)
= 12
Changed Price = Original price + Increased price
= 120+12
= Rs. 132
∴ The changed price of oil is Rs. 132
To find the changed price of Dal,
Original price = Rs. 80
Increased price = 10% of 80
![](data:image/png;base64,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)
= 8
Changed Price = Original price + Increased price
= 80+8
= Rs. 88
∴ The changed price of dal is Rs. 88
∴ The changed prices are as follows
![](data:image/png;base64,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)
Question 14.There were 2075 members enrolled in the club during last year. This year enrolment is decreased by 4% .
Find the decrease in enrolment.
Answer:Number of members enrolled in the club during last year = 2075
Decreased percentage of enrolment = 4%
Decrease in enrolment = 4% of 2075
![](data:image/png;base64,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)
= 83
∴ The decrease in enrolment is 83 members
Question 15.There were 2075 members enrolled in the club during last year. This year enrolment is decreased by 4% .
How many members are enrolled during this year?
Answer:Members enrolled this year = Members enrolled last year - decrease in enrolment
Number of members enrolled in the club during last year = 2075
Decrease in enrolment = 83
∴ Members enrolled this year = 2075 – 83
= 1992
∴ Members enrolled this year is 1992 members.
Question 16.A farmer obtained a yielding of 1720 bags of cotton last year. This year she expects her crop to be 20% more. How many bags of cotton does she expect this year?
Answer:Number of bags of cotton yielded last year = 1720
Expected crop in this year in % = 20% of 1720
20 % of 1720 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGkAAAAiCAMAAABrwwenAAAAAXNSR0IArs4c6QAAAIRQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGaQAGa2OgAAOgA6OjqQOmZmOmaQOma2OpDbZgAAZgA6ZjoAZjo6ZjpmZmaQZpDbZrbbZrb/kDoAkGY6kLbbkNv/tmYAtmY6ttv/tv//25A625Bm27Zm27aQ29u22////7Zm/9uQ/9u2//+2///b3wr0jgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABwUlEQVRIS+1W2XaCMBBNbLXQ1hbporRNNVVZkv//v86SIPQgVg7xyXmAHEjmZu7cSUaIqwVhYJ9K+QSe7YecvAdBcE7N4lNsJ19C6Cgv7+Ed1BDBJCths+egOBAOAJgFxKOisEhbTNMlkDQCXYK9AoCKFTA3C6wIk0gwQDKpnCz707R7IW1qXCHlLBd2ByUypY9QJPJhPU6aq1TebNCVgn2JMkYe5FJUCX612SyvMv5/pplXXlW5tyjna93wRGPSqkZGCizJAkdnm82mCGUS0gtbA8kkdemRf4XAJhlUJcjHn7UNJI0xsCEITYbZ+FScRrDDnP5AYfU+jWBpR0w2q3dPCWMkfnZajd4a+Kk2Q311Ih0ywifYSaRTQR1FguLjtS44zx5GOpC9VlB1nsrY60E5ep0iBp3QXhEN/mok8ktqxJ0U4J+lPlDlFE5LuF5wtcTpQrMKrwKQXY8g+tJUvXEwpXvDcRODbm7xWqYyJYGzkpAzOEHk/Jjy+vUw9l/7TYXhm4hwzcTPY0pIvokI2UxoRPJNRNBmgpFcExH0ir80kmvBQrJn1R0WgW8iwjUT1BJgibsm4h/NxNh1dvXXYOAXpdUr5bQrNZcAAAAASUVORK5CYII=)
= 344
Expected cotton bags in this year = Number of bags of cotton yielded last year + Expected crop
= 1720+344
= 2064 bags
∴ Expected cotton bags in this year is 2064 bags
Question 17.Points P and Q are both in the line segment AB and on the same side of its midpoint. P divides AB in the ratio 2:3, and Q divides AB in the ratio 3:4. If PQ = 2, then find the length of the line segment AB.
Answer:From the given, draw a line segment below
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAYEAAAAqCAYAAABV9ee9AAAAAXNSR0IArs4c6QAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAABPoSURBVHhe7V0JeBRF2n4nyeScXEASIIQkEG4IhMsVRORUWAi/oKCAsATQFVmERRQRRAFR8BeFfz1YwRU2KnIE5D6Xe7kCBiEiERKOkAtIMpA7k5m/vobWTqcnM5MJmM5UPU8/M9PTVV3fW9XvV/XVV1+7mFgCTxwBjgBHgCPgkAi4OKTUXGiOAEeAI8AREBDgSoB3BI4AR4Aj4MAIcCXgwI3PRecIcARqFwJlxorWfWcnTaVCciVQu/oAl4YjwBFwUATSc4oxfvnPuHqrCEbJUm9EkCdeHdAYfdvVUUSGKwEH7TBcbGUEiouLceXKFeTn58PHxwfh4eFwdnbmcHEEajwCxQYT4pPvoH9kXfRs5Y/SMpOgDA5dyMGo/zuH76dG4onW/hXk4Eqgxjdtza7gtdtF+Dk1H2Wsw0XU90SLhp41u8KV1O7o0aPYtGkT9Ho9NBoNjEYjgoODMWbMGDRp0kS1cvGKOwYCZPQh08/QroHCIabJT4ag/8IzWPGfVK4EHnZXyCsqY9rYWO621Eg+HurXvbkFBryz7jI2nMxCqcEokCZZI3u38ceikc0QUtf9YcNt1/12796NlStXom/fvujXrx98fX2RmZmJ7777DosWLcK7776L+vXr23UPnpkj8KARYI8hStjzKE+h9dyRqS95sOagguIy3GWkF+Tr+qDlVEX5tEAz4Z8/Y39iNpyoZViiLRluWie0DdHh9ehwNmXzU4Us8koWlhjZ9PI8m3rq8f7zEfhzVABcXTQ4/EsuZn77KwYvTsD2mVFo6O+mCvkyMjKwZs0a9O/fH+PHj/+tzv7+/pg+fbpwbNmyBRMnTlSFPLySjosAUU3WnRKksfUBMZ28pBdMQnOHNX2wSmB6bBI2HM/C9jej0LmJj+O2gkTyVGYqadXQC38fFCqcJVWQX2zE53uvY8TSn7D/7U7C/2pLXx24gaMXcwSi79b8d0UW3SkAkY290WPuKSyIS8Fn41uqQrTTp08Lpp8BAwZUqC+tC8yYMQNOTk6qkIVX0nERIAXg5eaM+XHJWLLtmjDopNn59awiDOocgOe6K89kq8UukZJViMMXcuGq1eDboxlcCdzvh7RA35yRPJGjND3W0g+dZ53A+uOZmDNUXbZmmmrGHk7H010CyykAUb6wAHe81K8RPtt1HbOHhqtiNpCSkoLAwEAEBJRvJ1Gm5s2bOy6zcMlVgwDxTRGbpcc8EYyn2tcVFobJTJucWYAV+2/g9W+S8MHzzeDiXN5ltFqUwIYTWajrrcXkp0KwdMc1zBgcigZ+6jAFPMgWNmefIzNJMDvSc5VtdA+yTvaWfSO7GMlM6f+FdTRz6bEWfli8+YqwYKwGk9Ddu3eh0+mg1WrthYfn5wj8oQiUMjM0WWJ6tZG4gzLXUF8vLSYy99Fn/xSERyJ8y9XRbiVQwtySNsZnCQuCzz1aH4t+uIJNp27iZTYadPREmlkr07qEyXFmo0tKL8CLfcwTaU3FjhaES0pNCPQxv/bjxzqcq4sT9IWlNVWMcvVyc3MTXELJJMTNPqpoMl5JMwjQGJ84WZ5C6rgx05AJN+9UfCbtVgInL+txKaMAS8e0gJ+Xi+CCFHskHS/1Df5tQdRRW8zTzQmnmN/uXOZFQwqBZga38kqx7lgmOoZ7YwRTmmpLtLBN5vFC5ghgLpHJiBbGtc7qsKOTG+ilS5eQl5cn7A2Qp6SkJNy+fRtdunSBi4vdj4zampzXV2UISDeKUdXTc4vx0darqKvTon2oroI0dvfo7/+bgU7hPujc9N7DM4n5pEYz75CjF/XowWzfjpycGVveZG5ZR5jXDO3mpoUaT7ZwM3VgY0zoFSwoTbUlMmNRZzqfmme26r+yWQ51xLAAD1WI165dO2zevBnnzp1D9+7dK9R57dq1yM7ORufOnVUhD6+kYyJAz1xRqRHT/31RsMiI84G8QgP7rsGSF1ooum7bxULZbFT7n8QcuDDf9ylfXxRIjtwHc/JLEXcy0+GVQF6RAf3Y7r2vX25Ta3qlr6eLsCORFrXfiA4D/ab09cF01NHd+48WjiMb61Tj+dSiRQtERkZi9erVwuKwuBBM5qHt27cjISEBkyZN4msGtaYX105B6jET7SfMIkP8K0aNIEVQn7ntkzOKub07dimBPeey2QaEYrbQ4Idf0vIFZGkzVHvmJrjtx1uYOSTc4fcN3N8iUKt6Hc1kNsXfxLgvEvGPcS3vL/6a8MY3v+L9jSlIZ7Of7/7WFlq2d0ANicJCxMTEYNmyZViwYAHatm0rmIVSU1ORnJyM6Oho9OrVSw2i8Do6MALe7s4Y83gDmxGwSwl8w0Z8jzbzw5bXO5S7MS16PvLWSYEoXlLh4qfNKJrJQNpYIahfdRX/h5VD4SHWvNoOMZ8novvbp9CdeQN5ezjDwISNT7mLJkEeKGHuafSbZolqSDQDmDNnDo4cOYLz588jNzcXISEhGD58uDBL4IkjUFsRqLISuMBG/seYl8uHo5pVwKYZI4luLXwReyiN+aw2VPSQqa2ASuUqLClDMTOP1cZEbqD/nd8V65hZ6FhSLvT5Bkzqz2KUMHPQnp9uYexniVjMwkcMfzRINeK7urqid+/ewsETR8BREKiyEog9nAFX5v5ID708kQmEPF+ICGi7cp+2yiFMazPIFCpiCbPP6dgUrbamemxvCLkCy92B2zTywp87BsDTtfbKXlvblMtV8xFIvZaCq8mX4aJ1QUTzVqgbYN9Aq8pK4H/YNmTaCWtuM9CwRwIRyBYkwlXiIVLdTU+KUClsa3Xfp6aWR7NBnjgCHIHqQyAjPQ3vzH4Tm/fHI9fgCY3JgED3Eowe9hRmzn4XXmzDY1VSlZVAl/suoeZuSjEsaOsyTxwBjgBHgCNgHwLXr11B9OBoJNwMguejb8Hdl+0xMhmRfisFC5Z/gTMJT2PNug3w9rY9bluVlYB9IvHcakAg/cY1FObnoV5gffj4qdekV1ZWJoSE3rZtG7KystiDwoLc9eiBcePGoU4d9cqlhj7E61g9CEydMhkJuWEIfGYeYCiGqYzt/GXWBt/QKJQFf4rtayfjg/lz8d7ij22+IVcCNkNWPkPShfM491MCDKWlaNW6DSI7drWzxD8+++4dW/HJJ5/g7KUMFLC+FqhzQu/unTBr9lyEhIb98RW0oQa0yYteCnPgwAE0bdpUeE9AWlqa8I6AL7/8ErGxsXwTmA148kurDwHah0J7q+jT3HcKAHf6xFFsOZoE3wFLgdJCpgDuxxyjDagl+XB29YRHzyn4as27mDp9BgKCGtpUSYtK4GrKZSScPsnetpSLRiGN0fXRHtBVYcphU61UcHFmRhpem/o3bD2cCL1TPbYjzwk64y30aNsASz5eipat26pAiopVXLZkMf7+9hKUtR4NXedH4OTqgWt3buKLPRuxe29vxMWtRfsodeycNRgMmDBhAk6cOCG4elKMIHrY6MGKiorC8ePH8eyzz+Lw4cNo1IjHurKnwwphi+8fVI6U1JSIzhL5if+by0uzO5E8pZ/mzld2Ld1DKZ/8nPS3/LtYRmXliP9JZbP0nYIanjtzAka/ZnDzZjzDlIA8mUqL4FkvFFklOly8kFh9SqC0tATvvTMHX8ZuREZZPRhdPKAtyUabIA3mvPkahg4faU+fUXXe9LRURA8ajPjMQOgefx91fIKEuECl+bnYEb8GiU8NwvZtm9CmXQdVybl/7y5Mn/sxXPsshE9YJzbKKBDsju4+gfBh087k/Z9hXMwEHDp8iEXdtN32+LDB2LFjB/bt24chQ4YIMX/o/cFiokBx3bp1E14nuWTJEuEQk5TMpOSmRHRKIzhLBKZEkNI8RBbib2vISSQ4SwQo/i8t3xYCtbZ8uXyVEZ0cK6Xf5s7ReUpK7SU9L7/OUvsq9VOxDGv7MA00KktK/yudIyWQnp4OjS8LOV9ZmRonmDTOKCmxPTKx4kygrMyAv06MwVfrT8Oz31vwD2wGjZMLjEzjnE06iGFjXsVqFnXxhXGO+aaluXNmIT6tDgKe/QCaMrLPMeBZf3TT+SOo/2u4tsuEqVOnYs++A9b2mYdyXaUPAxshkwnI0PRp1A3rDGNhzu91MhoAZoOs91gMflx3CrFfr8CIUeOEDmfNlLaykWBloysqW05c0t/myI+uoQdq1apVCA0NFcJEFxUVlcNYrHeHDh2wfv164RraOUyzB6VRo9I5kUxsIT1LCkBKeEoEZ+lcZQQnzysFhPIJrwgV4w3IeqSUoMTv1p6jopSulZ6n/205SIlLrxfLMleGeD19iod4LbU7fVe6RnofaT6l73SOyhL/o+9i2fLzStdK84nfPTw8kBB/DDM/WQ9DETP9UABDeh4lSeOsRUluBrxNejSNsP3dF4pKIHbVCny19ij8n18JrYcPm4KwESFTDM4sKmRgVDRyPetg6sx56Nm7DxqH1pyXoiiRnDUjAnMPuPw8dZRrVy4jbtdx6HouYAqgBCa2SPPbCJJ+s81h/t1jcHDzy1i1cjlaR3b8jSzl5SkRWmXEZi6/1KaoNIqUkrCSrCRXwd072H/8LHz6jL3X3vLEOp6Tmwdcmz6Gjz76GCfif2IhpUsr2DOViNEc8UnbSzoKl3+XElNleaTXkUwU86dr165CHZUSYUXhIXJycoQAcl5eXuVI0BJxyUlMvIc5chRJR0pYIslIz9GsRUq0lsiO8srJTUo+IsGJxCP9Lc8n/a1Uppy8lIhLfs4cEVI9pORo7t6V1Ukqk5TM5XlEDKVELz8nVQRypSBtu4cyYpPcpE/vXli74QfEJ2xCEOMWY5GeDTrvRfHVOLF3YDArzd0TsXiuRyQah0fYXL0KSsBoLMO/Vn8HTYdRcPXyZze883uh7MbGwlz4NuuGrAutsXjhAowe96IwzbZEUOKoztw019JUU6l8KsvWfFKSlU9T5VN/kbzE8/RwXku+CL3JB37+jX5foJHCzojF1dMXJr9wLJg/D01btis3RasKoSnlEZWbzS0uG5VRfnp4CvL0QvA/Hy2L/MlMQIqJ4e3CBgU5uXpcvXpViBQqJUKRjKSkJR1JiQ+8LSM+pYfXGrJwd3cXIn/q9Xqz7wigcih8NHkI0ZoB5RFlkNZVOqKTk460LlISkpObPWRnjbxSnM3hXxnulJ+nmomAk7MLPvrfRRg0dDQynZxRL+pptlZ3b09AaeEd5Bz4AuGmM1j4wa5yMy5rpamgBHJu38T1mwXwaNmSjQjLT6F/K5TsxKGd8P26T/FrSioM922Y4v/y0Zo1ozdL5GitQLaM3uQEZi6veB0pAXoLlYkpAUsRcUgeL09P0MvKycSgNOqQjzzMjdAsjYQqIwmlMuWEJMTIZ8p//sIPkJF9nbmDspfdkAuaPDG7Y0HaRQwb8CTGvzQZpWwmIB31KY3sbJVJJDMlQlUaScuJTWwrsqW2bt0aU6ZMQfv27QVFRwMGMYl1pfDRgwYNwqxZs6ztYvw6jsBDR+DxJ/pia9w37H3Xr+Nk3E5AFyaYhZwLrqJ/hwYs+OEWhDetGMLHmopWUAICuTGSv0fK5qnOxKbYNHIKqBfAAoXde7ikoxFz36tKCpZGQ/JyRaIzNyKz9n8pyZF3SUbadYx5eQYKs1PhGRBaQVHS2klJARt96lPwzufz0YV5U5ESMDftltbbmhGySHJK11rT4JVdc/3KJbyz/FvomvwJTs6u5WY6Tu7eyM/4FS5Zx/DajB8QqQIPoREjRgjrArt27cLAgQMF7yBSBGLfPHPmjDCLnTZtmr3Q8fwcgQeOwONP9MH+AwdxaP9uJF28yKL0atGWBTfs3rMP69NVD9FSQQn41w1AeH0fJN84D59G7RgR/G7zFqSkFWo2IixOOYlxY0bjlWmvC+YOOZmJpCcnZ3G0LZ++Pkhyq9bW6dgRwzbG4Z/bvoDHMx9C48Je23bfb5fscxqtJ5uefY5+7YMxZOhwBpV6ptmTp72Gbbv24NTW9+Df51VomVnrXjIhj80A8nfOxZwpI1WhAKjWFBBuxYoVGDlypOAFFBERAT8/P2GRmN4kRn2Q9gk0a1a1EVS19iteGEfACgQ8vXR4atBQdlhxsZWXVJwJMI0yIWYs9r04F8Utewu+qcZS9q4AmhjQyrqbD7IT9yAIlzHx5ZUICrIveJGV9axRl81b8D5+TBiIUz/Mhs/jf4Wrd4CgHEvZDCD35OcIyT/IXA43q0oBEMB12QAgbkMcJrLY+rs2T4KpDguh7OYN6FOhy/8Zb01+BvPeW1yj2sJSZcLCwrB3714sX74cO3fuxI0bN4TFYJolvPLKKwgPD7dUBP+fI1CrEVD0DhoxaiyOHD2CT1dNglvvN+DVsA0zDzCbakkRcs6ugcvZ5fjHv5ax3aOO+QAFNWiIbTuYT/20Kdi0bzpuaViMJOaj627IQnSXCHz40U40b9lalR2nUeMwbN+zFzu2bMQRtokqj7kCN2zQBYOHLESbyChVyuTJ1mbI5EMHLfbzRVBVNiOv9ANCQFEJkMlm2afLER72Pj5duRRX47Vss5gXtMW30TVMh3nrv8aTAwc/oCqpo9iAwCCs/uZ7tkPvHH5JPM8Wxw3stYSt0E4FtnJLCGuYuW9g9DDhqG2JK4Da1qJcHnsRMBs2ghYapr8xGy+MjUHiuQT2pqUcBAeHoH3HLnBzV8cLxO0Fx5r8LVq1Ax08cQQ4AhwBNSJgMXZQYP2GoIMnjgBHgCPAEah9CFhUArVPZC4RR4AjwBHgCIgIcCXA+wJHgCPAEXBgBLgScODG56JzBDgCHAGuBHgf4AhwBDgCDowAVwIO3PhcdI4AR4Aj8P+sKlY/3AmqPAAAAABJRU5ErkJggg==)
Let the length of the line segment AB = X
P divides AB in the ratio = 2:3
Thus the length of AP = ![](data:image/png;base64,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)
The length of PB = AB-AP
![](data:image/png;base64,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)
![](data:image/png;base64,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)
∴PB![](data:image/png;base64,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)
Q divides AB in the ratio = 3:4
Thus the length of AQ = ![](data:image/png;base64,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)
The length of QB = AB-AQ
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACsAAAAsCAMAAADLhrFKAAAAAXNSR0IArs4c6QAAAFpQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOgBmOjpmOjqQOma2OpC2OpDbZgAAZgA6ZmY6ZmZmZrb/kDoAkNv/tmYAttv/tv//25A627Zm2////7Zm/9uQ//+2///bnlD2DAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAA80lEQVRIS81U2xaCIBBcLO2mlUiSIP//m+3iJXtwQTt1nAcODwO7MzALsG3opALQQogSjBD7hunWZsSFp8hxVSlHbYu75zq5q8Eeas4DlRvPBZulTpYc1Zyangs6uZ05anutYOC2BXYxDydREHI11XbSy5sDetSBuPqi2IvpkkHbsUZ5ga/Qcb0H2hdg4N8NND0YynuwrgmRVKiLhCnab/tHbrU7tK7HSgfH85PNQrFf97Cw3g/pNHMQ7MQZyisKg80CkZg0q4O5HMltweX904AudFFwMpT29zUmFPZJRRVlmD9gs3hl4UG2yrBhAkdZ9hfSCwyTCoVmftW4AAAAAElFTkSuQmCC)
∴QB![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACoAAAAiCAMAAAAeTrsEAAAAAXNSR0IArs4c6QAAAGNQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOgA6OjoAOjo6OjpmOma2OpDbZgAAZjoAZjpmZrbbZrb/kDoAkDo6kDqQkGaQkNv/tmYAtmY6tv//25A629uQ2////7Zm/9uQ//+2///bwPLLRgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAsUlEQVQ4T82RyxbCIAxEQ6v4KGoFtRb7yP9/pQM9x10jtQucDSxuJpOEKJO8UoYaVcrtB30lYlu2NOweIspuD5TGk2EXPoJ8bSMx6IORyb7iCaUnIkgaLy3b+t7B9Xje4JkXJofAoAZxv+w/BmALzKtaZl8aIbFSuKoi01lXtG3iXoIK+dQzPT7l02d5krUBlnfMW8E27GmbEoJvHbFLPktfpZgGZolpUtJ/ME0d/mfuDT6aCKNEJiwnAAAAAElFTkSuQmCC)
The length of PQ in the line segment = AQ-AP
![](data:image/png;base64,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)
by solving this,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Given, PQ = 2
∴ ![](data:image/png;base64,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)
X = 35×2
∴X = 70
The length of the line segment AB is 70 cm
Find the ratio of the following
Smita works in office for 6 hours and Kajal works for 8 hours in her office. Find the ratio of their working hours.
Answer:
Number of working hours of smita = 6 hours
Number of working hours of kajal = 8 hours
The formula for finding the ratio of their working hours is as follows
∴ The ratio of their working hours is 3:4
Question 2.
Find the ratio of the following
One pot contains 8 litre of milk while other contains 750 milliliter.
Answer:
One pot of milk = 8 litre
Other pot of milk = 750 milliliter
The formula for finding the ratio is as follows
1 litre = 1000 milliliter
∴ 8 litre = 8000 milliliter
= 32:3
∴ The ratio is 32:3
Question 3.
Find the ratio of the following
speed of a cycle is 15km/h and speed of the scooter is 30km/h.
Answer:
Speed of a cycle = 15km/h
Speed of the scooter = 30km/h
The formula for finding the ratio between the speed of cycle and the scooter is as follows
∴ The ratio of their working hours is 1:2
Question 4.
If the compound ratio of 5:8 and 3:7 is 45:x. Find the value of x.
Answer:
The compound ratio of 5:8 and 3:7 = 45:x
Here from the given ratios, a = 5,b = 8,c = 3 and d = 7.Then
If a:b and c:d are any ratios, then their compound ratio =
So, ac:bd
⇒
⇒
⇒
⇒
⇒ X = 168
∴ The Value of X is 168
Question 5.
If the compound ratio of 7:5 and 8:x is 84:60. Find x.
Answer:
The compound ratio of 7:5 and 8:x = 84:60
Here from the given ratios, a = 7,b = 5,c = 8 and d = X.Then
If a:b and c:d are any ratios, then their compound ratio =
So, ac:bd
⇒
⇒
⇒
⇒
⇒
⇒
⇒ X = 8
∴ The Value of X is 8
Question 6.
The compound ratio of 3:4 and the inverse ratio of 4:5 is 45:x. Find x.
Answer:
The compound ratio of 3:4 and the inverse ratio of 4:5 = 45:x
The inverse ratio of 4:5 = 5:4
Here from the given ratios, a = 3,b = 4,c = 5 and d = 4.Then
If a:b and c:d are any ratios, then their compound ratio =
So, ac:bd
⇒
⇒
⇒
⇒
⇒ X = 48
∴ The Value of X is 48
Question 7.
In a primary school there shall be 3 teachers to 60 students. If there are 400 students enrolled in the school, how many teachers should be there in the school in the same ratio?
Answer:
Number of teachers for 60 students = 3
Number of teachers for 400 students = X
The ratio of students = 60:400
The ratio of teachers = 3:X
The ratio of teachers = The ratio of students
60:400 = 3:X
⇒
⇒
⇒X = 20
∴ There are 20 teachers for 400 students in the school
Question 8.
In the given figure, ABC is a triangle. Write all possible ratios by taking measures of sides pair wise.
(Hint: Ratio of AB:BC = 8:6)
Answer:
In the given triangle, the measurement of the side AB = 8 cm
The measurement of the side BC = 6 cm
The measurement of the side AC = 10 cm
∴ The ratio of AB:BC =
∴ The ratio of AB:AC =
∴ The ratio of BC:AC =
∴ The ratio of BC:AB =
∴ The ratio of AC:AB =
∴ The ratio of AC:AB =
∴The Possible ratios are
Question 9.
If 9 out of 24 students scored below 75% marks in a test. Find the ratio of student scored below 75% marks to the student scored 75% and above marks.
Answer:
Given that the total number of students = 24
Number of students scored below 75% marks in a test = 9
Number of students scored 75% and above marks in a test = The total number of students - Number of students scored below 75% marks
⇒ 24-9 = 15
∴The ratio of student scored below 75% marks to the student scored 75% and above marks is
Question 10.
Find the ratio of number of vowels in the word’ MISSISSIPPI’ to the number of consonants in the simplest form.
Answer:
The number of vowels in the word’ MISSISSIPPI’ = 4(I) = 4
The number of consonants in the word’ MISSISSIPPI’ = (1M,4S,2P) = 7
Or
The number of vowels in the word’ MISSISSIPPI’ = (I) = 1
The number of consonants in the word’ MISSISSIPPI’ = (M,S,P) = 3
∴ The ratio is 4:7 or 1:3
Question 11.
Rajendra and Rehana own a business. Rehana receives 25% of the profit in each month. If Rehana received 2080 in particular month, what is the total profit in that month?
Answer:
The % of profit received by rehana in each month = 25%
The amount received by rehana at particular month = 2080
Let the total profit = X
25% of X = 2080
Here % compares every number to 100,
X = 8320
∴ The total profit in that month is Rs. 8320
Question 12.
In triangle ABC, AB = 2.2 cm, BC = 1.5 cm and AC = 2.3 cm. In triangle XYZ, XY = 4.4 cm, YZ = 3 cm and XZ = 4.6 cm. Find the ratio AB:XY, BC:YZ, AC:XZ. Are the lengths of corresponding sides of ΔABC and ΔXYZ are in proportion?
[Hint: Any two triangles are said to be in proportion, if their corresponding sides are in the same ratio]
Answer:
Given that,
In triangle ABC,
AB = 2.2 cm
BC = 1.5 cm
AC = 2.3 cm
In triangle XYZ,
XY = 4.4 cm
YZ = 3 cm
XZ = 4.6 cm
To Find the ratio AB:XY,
∴ The ratio of AB:XY =
To Find the ratio BC:YZ,
∴ The ratio of BC:YZ =
To Find the ratio AC:XZ,
∴ The ratio of AC:XZ =
∴ The ratios of AB:XY, BC:YZ, AC:XZ are ,
,
Here, the lengths of corresponding sides of ΔABC and ΔXYZ are in proportion because their corresponding sides are in the same ratio .
Question 13.
Madhuri went to a super market. The price changes are as follows. The price of rice reduced by 5% jam and fruits reduced by 8% and oil and dal increased by 10%. Help Madhuri to find the changed prices in the given table.
Answer:
To find the changed price of Rice,
Original price = Rs. 30
Reduction = 5% of 30
= 1.5
Changed Price = Original price – Reduction
= 30-1.5
= Rs. 28.5
∴ The changed price of rice is Rs. 28.5
To find the changed price of Jam,
Original price = Rs. 100
Reduction = 8% of 100
= 8
Changed Price = Original price – Reduction
= 100-8
= Rs. 92
∴ The changed price of jam is Rs. 92
To find the changed price of Apples,
Original price = Rs. 280
Reduction = 8% of 280
= 22.4
Changed Price = Original price – Reduction
= 280-22.4
= Rs. 257.6
∴ The changed price of apples is Rs. 257.6
To find the changed price of Oil,
Original price = Rs. 120
Increased price = 10% of 120
= 12
Changed Price = Original price + Increased price
= 120+12
= Rs. 132
∴ The changed price of oil is Rs. 132
To find the changed price of Dal,
Original price = Rs. 80
Increased price = 10% of 80
= 8
Changed Price = Original price + Increased price
= 80+8
= Rs. 88
∴ The changed price of dal is Rs. 88
∴ The changed prices are as follows
Question 14.
There were 2075 members enrolled in the club during last year. This year enrolment is decreased by 4% .
Find the decrease in enrolment.
Answer:
Number of members enrolled in the club during last year = 2075
Decreased percentage of enrolment = 4%
Decrease in enrolment = 4% of 2075
= 83
∴ The decrease in enrolment is 83 members
Question 15.
There were 2075 members enrolled in the club during last year. This year enrolment is decreased by 4% .
How many members are enrolled during this year?
Answer:
Members enrolled this year = Members enrolled last year - decrease in enrolment
Number of members enrolled in the club during last year = 2075
Decrease in enrolment = 83
∴ Members enrolled this year = 2075 – 83
= 1992
∴ Members enrolled this year is 1992 members.
Question 16.
A farmer obtained a yielding of 1720 bags of cotton last year. This year she expects her crop to be 20% more. How many bags of cotton does she expect this year?
Answer:
Number of bags of cotton yielded last year = 1720
Expected crop in this year in % = 20% of 1720
20 % of 1720
= 344
Expected cotton bags in this year = Number of bags of cotton yielded last year + Expected crop
= 1720+344
= 2064 bags
∴ Expected cotton bags in this year is 2064 bags
Question 17.
Points P and Q are both in the line segment AB and on the same side of its midpoint. P divides AB in the ratio 2:3, and Q divides AB in the ratio 3:4. If PQ = 2, then find the length of the line segment AB.
Answer:
From the given, draw a line segment below
Let the length of the line segment AB = X
P divides AB in the ratio = 2:3
Thus the length of AP =
The length of PB = AB-AP
∴PB
Q divides AB in the ratio = 3:4
Thus the length of AQ =
The length of QB = AB-AQ
∴QB
The length of PQ in the line segment = AQ-AP
by solving this,
Given, PQ = 2
∴
X = 35×2
∴X = 70
The length of the line segment AB is 70 cm
Exercise 5.2
Question 1.In the year 2012, it was estimated that there were 36.4 crore Internet users worldwide. In the next ten years, that number will be increased by 125%. Estimate the number of Internet users worldwide in 2022.
Answer:Internet users in the year 2012 = 36.4 crore
% of Increase in the next ten years = 125%
125% of 36.4 ![](data:image/png;base64,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)
= 45.5
Number of Internet users in the year 2022 = Number of Internet users in the year 2012 + Increased users
= 36.4+45.5
= 81.9 crore
∴ The number of Internet users worldwide in the year 2022 is 81.9 crore
Question 2.A owner increases the rent of his house by 5% at the end of each year. If currently its rent is Rs. 2500 per month, how much will be the rent after 2 years?
Answer:Rent of the house = Rs. 2500
% of Increase in each year = 5%
Rent increase in first year :
5% of 2500 ![](data:image/png;base64,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)
= 125
Rent increase in first year = Rent of the house + increase in %
= 2500+125
= Rs. 2625
Rent increase in second year :
5% of 2625 ![](data:image/png;base64,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)
= 131.25
Rent increase in second year = Rent of the house in first year + increase in %
= 2625+131.25
= Rs. 2756.25
∴ The rent after 2 years is Rs. 2756.25
Question 3.On Monday, the value of a company’s shares was Rs. 7.50. The price increased by 6% on Tuesday, decreased by 1.5% on Wednesday, and decreased by 2% on Thursday. Find the value of each share when trade opened on Friday.
Answer:The value of a company’s shares on Monday = Rs. 7.50
To find the value of a company’s shares on Tuesday,
Value on Monday = Rs. 7.50
% Increase = 6% of 7.50
![](data:image/png;base64,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)
= 0.45
Value on Tuesday = Value on Monday + value on Increase percentage
= 7.50+0.45
= Rs. 7.95
∴ The Value on Tuesday is Rs. 7.95
To find the value of a company’s shares on Wednesday,
Value on Tuesday = Rs. 7.95
% decrease = 1.5% of 7.95
![](data:image/png;base64,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)
= 0.11925
Value on Wednesday = Value on Tuesday - value on decrease percentage
= 7.95-0.11925
= Rs. 7.83075
∴ The Value on Wednesday is Rs. 7.83075
Value on Thursday = Rs. 7.83075
% decrease = 2% of 7.83075
![](data:image/png;base64,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)
= 0.156
Value on Thursday = Value on Wednesday - value on decrease percentage
= 7.83075-0.156
= Rs. 7.674
∴ The Value on Thursday is Rs. 7.674
The value of share when opened on Friday is equal to the Thursday’s closing price.
∴ The opening Value of the share on Friday is Rs. 7.674
Question 4.With most of the Xerox machines, you can reduce or enlarge your original by entering a percentage for the copy. Reshma wanted to enlarge a 2 cm by 4 cm drawing. She set the Xerox machine for 150% and copied her drawing. What will be the dimensions of the copy of the drawing be?
Answer:The original size of the drawing = 2cm × 4cm
Size to be enlarged = 150%
Enlarged new size = 150% of 2cm × 4cm
150% of 2cm = ![](data:image/png;base64,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)
= 3 cm
150% of 4cm = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADUAAAAiCAMAAADI62FhAAAAAXNSR0IArs4c6QAAAHJQTFRFAAAAAAAAAAA6ADpmADqQAGaQAGa2OgAAOgA6OjqQOmZmOma2OpDbZgAAZgA6ZjoAZjpmZmZmZmaQZpDbZrbbZrb/kDoAkDo6kGY6kNv/tmYAtmY6tv//25A625Bm29u22////7Zm/9uQ/9u2//+2///bi/tf6QAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABI0lEQVRIS9WU3XKCMBCFN/6ArSCtLVRRFDB5/1d0N5ugHQc34cIZz01mmHzJYXdzAN5A5pCQy0YpNdsDmJ2a/Yi2T58FUyVvbZK2XyEtqbmndF6CqTKJodO9wzWA3uA9tf3yXEyh+rScQJGzUIemXrZYur+9vQvqRUg1qOIqA3PAwv+iTV3wOqKGuhOrPpUo/XW0h17cSkbyb4ky1ZwwnWNDnOqskyjs9qJF6Na87qOVKcLORYIVZtEEMEUVfJTfZyqF1znZQUPKT+xoJf9RnT/dzfkYZR3eLqNt8n/5agweQygLUeXvX4A4G5ctX9K71RrkBz9VLjd8XkTmhsuLqNzwrzH0VXJu+LyIy42JlEu0UIecG0NeROXGkBdCbkzt74u5K/o5Ghr9Cii4AAAAAElFTkSuQmCC)
= 6 cm
∴ The dimensions of the copy of the drawing is 3 × 6 cm
Question 5.The printed price of a book is Rs. 150. And discount is 15%. Find the actual amount to be paid.
Answer:The printed price of a book = Rs. 150
Discount = 15%
= 15% of 150
![](data:image/png;base64,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)
= 22.5
The actual amount to pay = printed price of a book – discount
= 150-22.5
= Rs. 127.50
∴ The actual amount to be paid is Rs. 127.50
Question 6.The marked price of an gift item is Rs. 176 and sold it for Rs. 165. Find the discount percent.
Answer:Market price = Rs. 176
Sale price = Rs. 165
Discount = Market price - Sale price
= 176-165
Discount = 11
![](data:image/png;base64,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)
Discount percent = ![](data:image/png;base64,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)
= 6.25% or 6
%
∴ The discount percent of an gift item is 6
%
Question 7.A shop keeper purchased 200 bulbs for Rs. 10 each. However 5 bulbs were fused and put them into scrap. The remaining were sold at Rs. 12 each. Find the gain or loss percent.
Answer:Number of bulbs purchased at Rs. 10 = 200
Purchase price = 200 × 10 = Rs. 2000
If 5 bulbs were defective, remaining bulbs = 195
Sale price = 12
Sale price of 195 bulbs = 195×12 = Rs. 2340
Profit = sale price – purchase price
= 2340 – 2000
= Rs. 340
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= 17%
∴ The gain percent is 17%
Question 8.Complete the following table with appropriate entries (Wherever possible)
![](data:image/jpeg;base64,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)
Answer:1) Given that, cost price = ‘ 750
Expense = Rs. 50
Profit = Rs. 80
Selling price = cost price+ Expense + profit
= 750+50+80
∴ selling price = Rs. 880
Purchase price = cost price+ Expense
= 750+50
= Rs. 800
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= 10%
∴ Profit percent = 10%
2) Given that, cost price = ‘ 4500
Expense = Rs. 500
Loss = Rs. 1000
Selling price = cost price+ Expense - loss
= 4500+500-1000
∴ selling price = Rs. 4000
Purchase price = cost price+ Expense
= 4500+500
= Rs. 5000
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= 20%
∴ loss percent = 20%
3) Given that, cost price = ‘ 46000
Expense = Rs. 4000
Selling price = Rs. 60000
Purchase price = cost price+ Expense
= 46000+4000
= Rs. 50000
Profit = selling price – purchase price
= 60000- 50000
= Rs. 10000
∴ profit = Rs. 10000
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= 20%
∴ Profit percent = 20%
4) Given that, cost price = ‘ 300
Expense = Rs. 50
Profit percent = 12%
Purchase price = cost price+ Expense
= 300+50
= Rs. 350
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= Rs. 42
∴ Profit = Rs. 42
Selling price = purchase price + profit
= 350 + 42
= Rs. 392
∴ Selling price = Rs. 392
5) Given that, cost price = ‘ 330
Expense = Rs. 20
Loss percent = 10%
Purchase price = cost price+ Expense
= 330+20
= Rs. 350
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= Rs. 35
∴ loss = Rs. 35
Selling price = purchase price - loss
= 350 - 35
= Rs. 315
∴ Selling price = Rs. 315
![](data:image/png;base64,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)
Question 9.A table was sold for Rs. 2,142 at a gain of 5%. At what price should it be sold to gain 10%.
Answer:Selling price = Rs. 2142
Profit percent = 5%
Let the cost price of the table = X
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Selling price = cost price + profit
⇒![](data:image/png;base64,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)
⇒![](data:image/png;base64,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)
⇒![](data:image/png;base64,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)
⇒![](data:image/png;base64,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)
∴ cost price = Rs. 2040
Then, For the profit of 10%
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= Rs. 204
Selling price = cost price + profit
= 2040+204
= 2244
∴ The selling price of the table at 10% profit isRs. 2244
Question 10.Gopi sold a watch to Ibrahim at 12% gain and Ibrahim sold it to John at a loss of 5%. If John paid Rs. 1,330, then find how much did Gopi sold it?
Answer:Given that,
Profit percent of gopi = 12%
S.P of Ibrahim = Rs. 1330
Loss percent of Ibrahim = 5%
Let the cost price of gopi = X
S.P of Gopi = C.P of Ibrahim = 12%
![](data:image/png;base64,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)
= 0.12X
Selling price = cost price + profit
⇒![](data:image/png;base64,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)
⇒![](data:image/png;base64,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)
⇒![](data:image/png;base64,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)
∴ S.P of gopi = 1.12X = C.P of Ibrahim
To find the S.P of Ibrahim,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= 0.056X
∴ loss = 0.056X
Selling price = Cost price - loss
= 1.12X – 0.056X
= 1.064X
∴ Selling price of ibrahim = 1.064X
Given, S.P of Ibrahim = Rs. 1330
⇒1.064X = 1330
⇒![](data:image/png;base64,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)
X = 1250
∴ The cost price of gopi is Rs. 1250
Question 11.Madhu and Kavitha purchased a new house for Rs. 3,20,000. Due to some economic problems they sold the house for Rs. 2, 80,000.
Find (a) The loss incurred (b) the loss percentage.
Answer:Given that, C.P of house = Rs. 3,20,000
S.P of house = Rs. 2,80,000
(a) loss = cost price – selling price
= 320000 – 280000
= 40000
∴ The loss incurred is Rs. 40000
(b)![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEgAAAAsCAMAAADxVg45AAAAAXNSR0IArs4c6QAAAGxQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OjoAOjqQOmaQOma2OpDbZgAAZgA6ZjoAZmZmZrbbZrb/kDoAkGY6kLbbkNv/tmYAttv/tv//25A627Zm27aQ2////7Zm/9uQ/9u2//+2///b1Rw2WQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABZklEQVRIS+2W4U7DMAyE48FW2FgHrGWBsqZp3/8dsZ0GhOTEkVYk0MiP6CZln3xu6qsxV7m61Yl8Ty3A9lVXyR4NFYOmZt375uZNU0nOWD8xyNHu4KipJMjuGWEsFTPWG02lQG7bM4icEWjd51WKMx5OwVT4O+15lQBNzZ570h0vBDmY1wyiHkVrssq9IN+ajRXObU+oDCmAOn7ytOVVBhRutv7Aguf0wj4xyT8C7PhkXl3lGPk3HTtg42sVbs3C6xNeLBYs4GetLVjo70RN7/cAt5ySZ5wlrMTg1cq3qxfjG7peFp6Nr1Nxq3GMxVQMA/ZLScGrgvgAj3xePLil4C0B+XbHHyIRKcVtAWes47jGw0OFBUl5WQDCI+dqtsbhewEIO0MAJFDnxbgtqwgdMchuQnZJcauRghl+VqajDHT4W4pbHYR30XOMDnf0hWMRJAWvBjK+rQAeyNI8a6hCKW5V0p8+8AHtFDLJwMHsJgAAAABJRU5ErkJggg==)
= 12.5
∴ The loss percentage is 12.5%
Question 12.A pre-owned car show-room owner bought a second-hand car for Rs. 1,50,000. He spent Rs. 20,000 on repairs and painting, then sold it for Rs. 2,00,000. Find whether he gets profit or loss. If so, what percent?
Answer:Purchase price of a car = Rs. 1,50,000
Repairs and painting = Rs. 20,000
Selling price = Rs. 2,00,000
Total cost price = purchasing price + Repair charges
= Rs. 1,50,000 + Rs. 20,000
= Rs. 1,70,000
∴ cost price = Rs. 1,70,000
Here, selling price > cost price, so there is a profit.
Profit = selling price - cost price
= 2,00,000 - 1,70,000
= 30,000
∴Profit = Rs. 30,000
On cost price of Rs. 1,70,000 profit is 30,000
If cost price is Rs. 100,profit will be?
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
= 17.65%
∴Profit percent = 17.65%
Question 13.Lalitha took a parcel from a hotel to celebrate her birthday with her friends. It was billed with Rs. 1,450 including 5% VAT. Lalitha asked for some discount, the hotel owner gave
8% discount on the bill amount. Now find the actual amount that lalitha has to pay to the hotel owner
Answer:The cost of parcel including 5% VAT = Rs. 1450
Discount given by the hotel owner = 8%
Actual discount = 8% of 1450
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHEAAAAsCAMAAABlsKfLAAAAAXNSR0IArs4c6QAAAIdQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOjoAOjpmOjqQOmaQOma2OpC2OpDbZgAAZgA6ZjoAZjo6ZjpmZmZmZmaQZpDbZrbbZrb/kDoAkDo6kGY6kLbbkNv/tmYAttv/tv//25A625Bm27Zm27aQ29u22////7Zm/9uQ/9u2//+2///bcFkebwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAB9klEQVRYR+2XbVPCMAyAVxSZgjLBF5jIcILspf//95k0TcsG5zzW1vO0H6DM254mTZ7OKPofvy8D22shBs8B150PFlG0FdNgSJmOkJVd7UMhmai4YUYhMKuDdRiaouxiqJyQwDKGosnFMliMMsWaoc8wo06oVi/ewvBMdAG7A7bwbh/UANAZYLnha6icuuK8++uu3dw8O1dNXEI3636WKyHGG1dB0HOqmTA1XcaayJ2MHValbmu+nGxyfmKdPLaIBf4uWCX1A7Vbpb/PDt0Qs6kiQFY5RtXSur2x64aIrJPbs1l0IxOL8b5FJG3VCctL/TYL6MRmWA5qtByvifX9OmLiTSyGEO2RLuHCx2zUW55ElCnYH4j5MpIvi6hKYV3HgpapsLY2IZycfJECIhZ8m95DPH84q/ZobxC70tqVVbyfsqqG2i5dOeaFSWW1/5FkapWJGRLsGWu6g2KGpfTdSBINla2aZvBJfY9las9ZPft+sZ5Mu1yh0i7p3Rb2EpHVHC5NNngFjCQmHFL1RLNSf3fto5+/s5StgH2o2K7dSNkK2IeKLdBK2Qq4qWIPidWFbgXcVLE3ohVwW8XukaxIfl/1/+b6s0RUw7GKXee1WTmgx7aKXQP5OFf/5CgB25lz1qGJDwTcVLFr6oGUrYAbKnZN/PPP+wQkJjeOv/A8egAAAABJRU5ErkJggg==)
= 116
∴ Actual discount = Rs. 116
The actual amount paid by lalitha = bill amount – actual discount
= 1450 – 116
= Rs. 1334
∴ The actual amount paid by lalitha is Rs. 1334.
Question 14.If VAT is included in the price, find the original price of each of the following.
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)
Answer:(i) Bill amount of diamond = Rs. 10100
VAT = 1%
Original price = Bill amount - VAT
= 10100 - 1% of 10100
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
∴ The original price of diamond is Rs. 9999
(ii) Bill amount of pressure cooker = Rs. 2940
VAT = 5%
Original price = Bill amount - VAT
= 2940 - 5% of 2940
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
∴ The original price of pressure cooker is Rs. 2793
(iii) Bill amount of face powder = Rs. 229
VAT = 14.5%
Original price = Bill amount - VAT
= 229 – 14.5% of 229
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
∴ The original price of face powder is Rs. 195.80(approximate)
Question 15.Find the buying price of each of the following items when a sales tax of 5% is added on them.
(i) a towel of Rs. 50
(ii) Two bars of soap at Rs. 35 each.
Answer:(i) cost of a towel = Rs. 50
Sales tax on a towel = 5% of 50
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAF0AAAAsCAMAAAAw0USVAAAAAXNSR0IArs4c6QAAAHVQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOjpmOjqQOmaQOma2OpDbZgAAZjoAZjo6ZjpmZmaQZpDbZrbbZrb/kDoAkDo6kGY6kNv/tmYAttv/tv//25A625Bm27aQ29u22////7Zm/9uQ/9u2//+2///bovOkmQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABeElEQVRYR+2XbVMCIRCAoTIpS+2N7Mws4fj/PzGWBZacy65hcZqKD3c65z0su8vDKMTvHy9PbdZolPTjpBn9oU3YgWrUP304vUZdKDlpVFThHu+F1a16Jpb2umHj9PNpG3oHURvVKPbOp9zq0+c2sdulF8Fs3Qb+s6hHkKlbSXnJm0zSndPnb5WN0N9gG9l4L2S6g529kzVudXoC+H5+FQtPsXfQv5UbENZfMjI9PPBP4NrBwRbGd03lKa+LqUfgyDJFOl4HR55x8EN6xWlZELJMv6SP20Mf6VmmKTMgvsrM7C0/1DJWtUp8qaopuyTTDTRjbUeGsKnxSKbQLgeKOibt9haDNvEuCpnahdfqZx2D8O0Sj2qSBp8+/PR4YpA0GPSRtsZsvUE6SYNBH5TySCdpcOgj45FO0ij1Mabsh39T0oHMtMHjpMejw54p9cGVmUIaHPrYq6ogaTDoo+hIPE1IGgz6iHS3gj9jZ3f+K0ljhD7qC/I3CO8KOScjIUBhUgAAAABJRU5ErkJggg==)
= Rs. 2.5
∴ sales tax on a towel = Rs. 2.5
Buying price = cost + sales tax
= 50+2.5
= Rs. 52.5
∴ The buying price of a towel = Rs. 52.5
(ii) cost of a soap bar = Rs. 35
Cost of two soap bars = 35×2 = Rs. 70
Sales tax on a soap bars = 5% of 70
![](data:image/png;base64,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)
= Rs. 3.5
∴ sales tax on a towel = Rs. 3.5
Buying price = cost + sales tax
= 70+3.5
= Rs. 73.5
∴ The buying price of a soap bars = Rs. 73.5
Question 16.A Super-Bazar prices an item in rupees and paise so that when 4% sales tax is added, no rounding is necessary because the result is exactly in ‘n’ rupees, where ‘n’ is a positive integer. Find the smallest value of ‘n’.
Answer:Let the final rupees of an item = n
Let the initial rupees before tax = x
Sales tax = 4%
Initial rupees + sales tax = final rupee
⇒ ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
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Here, n should be the factor of 26.so, the factor of 26 are 1,2,13,26.
For X to be terminating decimal, n can be either 13 or 26. 13 is smaller
∴ n = 13
In the year 2012, it was estimated that there were 36.4 crore Internet users worldwide. In the next ten years, that number will be increased by 125%. Estimate the number of Internet users worldwide in 2022.
Answer:
Internet users in the year 2012 = 36.4 crore
% of Increase in the next ten years = 125%
125% of 36.4
= 45.5
Number of Internet users in the year 2022 = Number of Internet users in the year 2012 + Increased users
= 36.4+45.5
= 81.9 crore
∴ The number of Internet users worldwide in the year 2022 is 81.9 crore
Question 2.
A owner increases the rent of his house by 5% at the end of each year. If currently its rent is Rs. 2500 per month, how much will be the rent after 2 years?
Answer:
Rent of the house = Rs. 2500
% of Increase in each year = 5%
Rent increase in first year :
5% of 2500
= 125
Rent increase in first year = Rent of the house + increase in %
= 2500+125
= Rs. 2625
Rent increase in second year :
5% of 2625
= 131.25
Rent increase in second year = Rent of the house in first year + increase in %
= 2625+131.25
= Rs. 2756.25
∴ The rent after 2 years is Rs. 2756.25
Question 3.
On Monday, the value of a company’s shares was Rs. 7.50. The price increased by 6% on Tuesday, decreased by 1.5% on Wednesday, and decreased by 2% on Thursday. Find the value of each share when trade opened on Friday.
Answer:
The value of a company’s shares on Monday = Rs. 7.50
To find the value of a company’s shares on Tuesday,
Value on Monday = Rs. 7.50
% Increase = 6% of 7.50
= 0.45
Value on Tuesday = Value on Monday + value on Increase percentage
= 7.50+0.45
= Rs. 7.95
∴ The Value on Tuesday is Rs. 7.95
To find the value of a company’s shares on Wednesday,
Value on Tuesday = Rs. 7.95
% decrease = 1.5% of 7.95
= 0.11925
Value on Wednesday = Value on Tuesday - value on decrease percentage
= 7.95-0.11925
= Rs. 7.83075
∴ The Value on Wednesday is Rs. 7.83075
Value on Thursday = Rs. 7.83075
% decrease = 2% of 7.83075
= 0.156
Value on Thursday = Value on Wednesday - value on decrease percentage
= 7.83075-0.156
= Rs. 7.674
∴ The Value on Thursday is Rs. 7.674
The value of share when opened on Friday is equal to the Thursday’s closing price.
∴ The opening Value of the share on Friday is Rs. 7.674
Question 4.
With most of the Xerox machines, you can reduce or enlarge your original by entering a percentage for the copy. Reshma wanted to enlarge a 2 cm by 4 cm drawing. She set the Xerox machine for 150% and copied her drawing. What will be the dimensions of the copy of the drawing be?
Answer:
The original size of the drawing = 2cm × 4cm
Size to be enlarged = 150%
Enlarged new size = 150% of 2cm × 4cm
150% of 2cm =
= 3 cm
150% of 4cm =
= 6 cm
∴ The dimensions of the copy of the drawing is 3 × 6 cm
Question 5.
The printed price of a book is Rs. 150. And discount is 15%. Find the actual amount to be paid.
Answer:
The printed price of a book = Rs. 150
Discount = 15%
= 15% of 150
= 22.5
The actual amount to pay = printed price of a book – discount
= 150-22.5
= Rs. 127.50
∴ The actual amount to be paid is Rs. 127.50
Question 6.
The marked price of an gift item is Rs. 176 and sold it for Rs. 165. Find the discount percent.
Answer:
Market price = Rs. 176
Sale price = Rs. 165
Discount = Market price - Sale price
= 176-165
Discount = 11
Discount percent =
= 6.25% or 6%
∴ The discount percent of an gift item is 6%
Question 7.
A shop keeper purchased 200 bulbs for Rs. 10 each. However 5 bulbs were fused and put them into scrap. The remaining were sold at Rs. 12 each. Find the gain or loss percent.
Answer:
Number of bulbs purchased at Rs. 10 = 200
Purchase price = 200 × 10 = Rs. 2000
If 5 bulbs were defective, remaining bulbs = 195
Sale price = 12
Sale price of 195 bulbs = 195×12 = Rs. 2340
Profit = sale price – purchase price
= 2340 – 2000
= Rs. 340
= 17%
∴ The gain percent is 17%
Question 8.
Complete the following table with appropriate entries (Wherever possible)
Answer:
1) Given that, cost price = ‘ 750
Expense = Rs. 50
Profit = Rs. 80
Selling price = cost price+ Expense + profit
= 750+50+80
∴ selling price = Rs. 880
Purchase price = cost price+ Expense
= 750+50
= Rs. 800
= 10%
∴ Profit percent = 10%
2) Given that, cost price = ‘ 4500
Expense = Rs. 500
Loss = Rs. 1000
Selling price = cost price+ Expense - loss
= 4500+500-1000
∴ selling price = Rs. 4000
Purchase price = cost price+ Expense
= 4500+500
= Rs. 5000
= 20%
∴ loss percent = 20%
3) Given that, cost price = ‘ 46000
Expense = Rs. 4000
Selling price = Rs. 60000
Purchase price = cost price+ Expense
= 46000+4000
= Rs. 50000
Profit = selling price – purchase price
= 60000- 50000
= Rs. 10000
∴ profit = Rs. 10000
= 20%
∴ Profit percent = 20%
4) Given that, cost price = ‘ 300
Expense = Rs. 50
Profit percent = 12%
Purchase price = cost price+ Expense
= 300+50
= Rs. 350
= Rs. 42
∴ Profit = Rs. 42
Selling price = purchase price + profit
= 350 + 42
= Rs. 392
∴ Selling price = Rs. 392
5) Given that, cost price = ‘ 330
Expense = Rs. 20
Loss percent = 10%
Purchase price = cost price+ Expense
= 330+20
= Rs. 350
= Rs. 35
∴ loss = Rs. 35
Selling price = purchase price - loss
= 350 - 35
= Rs. 315
∴ Selling price = Rs. 315
Question 9.
A table was sold for Rs. 2,142 at a gain of 5%. At what price should it be sold to gain 10%.
Answer:
Selling price = Rs. 2142
Profit percent = 5%
Let the cost price of the table = X
Selling price = cost price + profit
⇒
⇒
⇒
⇒
∴ cost price = Rs. 2040
Then, For the profit of 10%
= Rs. 204
Selling price = cost price + profit
= 2040+204
= 2244
∴ The selling price of the table at 10% profit isRs. 2244
Question 10.
Gopi sold a watch to Ibrahim at 12% gain and Ibrahim sold it to John at a loss of 5%. If John paid Rs. 1,330, then find how much did Gopi sold it?
Answer:
Given that,
Profit percent of gopi = 12%
S.P of Ibrahim = Rs. 1330
Loss percent of Ibrahim = 5%
Let the cost price of gopi = X
S.P of Gopi = C.P of Ibrahim = 12%
= 0.12X
Selling price = cost price + profit
⇒
⇒
⇒
∴ S.P of gopi = 1.12X = C.P of Ibrahim
To find the S.P of Ibrahim,
= 0.056X
∴ loss = 0.056X
Selling price = Cost price - loss
= 1.12X – 0.056X
= 1.064X
∴ Selling price of ibrahim = 1.064X
Given, S.P of Ibrahim = Rs. 1330
⇒1.064X = 1330
⇒
X = 1250
∴ The cost price of gopi is Rs. 1250
Question 11.
Madhu and Kavitha purchased a new house for Rs. 3,20,000. Due to some economic problems they sold the house for Rs. 2, 80,000.
Find (a) The loss incurred (b) the loss percentage.
Answer:
Given that, C.P of house = Rs. 3,20,000
S.P of house = Rs. 2,80,000
(a) loss = cost price – selling price
= 320000 – 280000
= 40000
∴ The loss incurred is Rs. 40000
(b)
= 12.5
∴ The loss percentage is 12.5%
Question 12.
A pre-owned car show-room owner bought a second-hand car for Rs. 1,50,000. He spent Rs. 20,000 on repairs and painting, then sold it for Rs. 2,00,000. Find whether he gets profit or loss. If so, what percent?
Answer:
Purchase price of a car = Rs. 1,50,000
Repairs and painting = Rs. 20,000
Selling price = Rs. 2,00,000
Total cost price = purchasing price + Repair charges
= Rs. 1,50,000 + Rs. 20,000
= Rs. 1,70,000
∴ cost price = Rs. 1,70,000
Here, selling price > cost price, so there is a profit.
Profit = selling price - cost price
= 2,00,000 - 1,70,000
= 30,000
∴Profit = Rs. 30,000
On cost price of Rs. 1,70,000 profit is 30,000
If cost price is Rs. 100,profit will be?
= 17.65%
∴Profit percent = 17.65%
Question 13.
Lalitha took a parcel from a hotel to celebrate her birthday with her friends. It was billed with Rs. 1,450 including 5% VAT. Lalitha asked for some discount, the hotel owner gave
8% discount on the bill amount. Now find the actual amount that lalitha has to pay to the hotel owner
Answer:
The cost of parcel including 5% VAT = Rs. 1450
Discount given by the hotel owner = 8%
Actual discount = 8% of 1450
= 116
∴ Actual discount = Rs. 116
The actual amount paid by lalitha = bill amount – actual discount
= 1450 – 116
= Rs. 1334
∴ The actual amount paid by lalitha is Rs. 1334.
Question 14.
If VAT is included in the price, find the original price of each of the following.
Answer:
(i) Bill amount of diamond = Rs. 10100
VAT = 1%
Original price = Bill amount - VAT
= 10100 - 1% of 10100
∴ The original price of diamond is Rs. 9999
(ii) Bill amount of pressure cooker = Rs. 2940
VAT = 5%
Original price = Bill amount - VAT
= 2940 - 5% of 2940
∴ The original price of pressure cooker is Rs. 2793
(iii) Bill amount of face powder = Rs. 229
VAT = 14.5%
Original price = Bill amount - VAT
= 229 – 14.5% of 229
∴ The original price of face powder is Rs. 195.80(approximate)
Question 15.
Find the buying price of each of the following items when a sales tax of 5% is added on them.
(i) a towel of Rs. 50
(ii) Two bars of soap at Rs. 35 each.
Answer:
(i) cost of a towel = Rs. 50
Sales tax on a towel = 5% of 50
= Rs. 2.5
∴ sales tax on a towel = Rs. 2.5
Buying price = cost + sales tax
= 50+2.5
= Rs. 52.5
∴ The buying price of a towel = Rs. 52.5
(ii) cost of a soap bar = Rs. 35
Cost of two soap bars = 35×2 = Rs. 70
Sales tax on a soap bars = 5% of 70
= Rs. 3.5
∴ sales tax on a towel = Rs. 3.5
Buying price = cost + sales tax
= 70+3.5
= Rs. 73.5
∴ The buying price of a soap bars = Rs. 73.5
Question 16.
A Super-Bazar prices an item in rupees and paise so that when 4% sales tax is added, no rounding is necessary because the result is exactly in ‘n’ rupees, where ‘n’ is a positive integer. Find the smallest value of ‘n’.
Answer:
Let the final rupees of an item = n
Let the initial rupees before tax = x
Sales tax = 4%
Initial rupees + sales tax = final rupee
⇒
Here, n should be the factor of 26.so, the factor of 26 are 1,2,13,26.
For X to be terminating decimal, n can be either 13 or 26. 13 is smaller
∴ n = 13
Exercise 5.3
Question 1.Sudhakar borrows Rs. 15000 from a bank to renovate his house. He borrows the money at 9% p.a. simple interest over 8 years. What are his monthly repayments?
Answer:Principal (P) = Rs. 15000
Time period (T) = 8
Rate of interest (R) = 9%
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I = Rs. 10800
∴ Interest for 8 years is Rs. 10800
Amount to be paid at the end of 8 years = Principal + interest
Amount = 15000+10800
= 25800
∴ Amount to be paid at the end of 8 years is Rs. 25800
![](data:image/png;base64,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)
⇒ monthly repayment = ![](data:image/png;base64,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)
= 268.75
∴ Sudhakar pays Rs. 268.75 monthly.
Question 2.A TV was bought at a price of Rs. 21000. After 1 year the value of the TV was depreciated by 5% (Depreciation means reduction of the value due to use and age of the item). Find the value of the TV after 1 year.
Answer:Cost price of TV = Rs. 21000
Depreciation = 5%
Depreciation after 1 year = 5% of 21000
![](data:image/png;base64,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)
∴ Depreciation after 1 year = Rs. 1050
Value of TV after 1 year = cost price – depreciation
= 21000 – 1050
= Rs. 19950
∴The value of TV after 1 year is Rs. 19,950
Question 3.Find the amount and the compound interest on Rs. 8000 at 5% per annum, for 2 years compounded annually.
Answer:Principal (P) = Rs. 8000
Time period (n) = 2
Rate of interest (R) = 5%
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= 8000×1.052
= 8820
∴ Amount = Rs. 8820
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= (8000×1.052)-8000
= 8820-8000
= 820
∴ Compound Interest = Rs. 820
Question 4.Find the amount and the compound interest on Rs. 6500 for 2 years, compounded annually, the rate of interest being 5% per annum during the first year and 6% per annum during the second year.
Answer:Principal (P) for 1st year = Rs. 6500
Rate of interest (R) for first year = 5%
Interest on first year = 5% of 6500
= ![](data:image/png;base64,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)
= 325
∴ Interest for 1st year = Rs. 325
Principal (P) for second year = Principal (P) for 1st year + Interest for 1st year
Principal (P) for second year = Rs. 6500 + Rs. 325 = Rs. 6825
Rate of interest (R) for second year = 6%
Interest on second year = 6% of 6825
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFMAAAAiCAMAAAAUEhVWAAAAAXNSR0IArs4c6QAAAJZQTFRFAAAAAAAAAAA6AABmADpmADqQAGaQAGa2OgAAOgA6OjoAOjo6OjpmOmZmOmaQOma2OpC2OpDbZgAAZgA6ZjoAZjo6ZjpmZmaQZpDbZrbbZrb/kDoAkDo6kGY6kLaQkLbbkNv/tmYAtmY6ttv/tv//25A625Bm27Zm27aQ29u229vb29v/2////7Zm/9uQ/9u2//+2///bZILLDgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABvklEQVRIS+1VaVfCMBBMOCReVGtRoV5BSkHpkf//55zdJJXn1T6aD76n+6GbQjOZndkkQvwHFMhn011YIczyIjCiENkkLEegmXQ6Ow1ce6mil20almt99YT6x0ElNWm0MyF4rsHNR5VIGbXTNEvFxeQnUg5uyYgNJo4IqFQSMdjD7OZ6oaJX+jIbzIErL4XQci6qeLgizEU7SH2NLxGVy0IUClDcJeymBmVNo0wCrhOmSUcEWseRW7+OXWN4TN8nRWdM0AGRBgg0aSpHgYpF3minO9dONY63yaRxTg8fvJMbGNJA2qpLdaasW+TV5/Bim1S+9yxecCZsFJwp6cEqsrp4QbqDW2m77x8wGR/OsChWmsYwS4MX+zG49oaow8iGK6cxywjn99p6T/2vkb1Hfo7D8Dy5l+yGLqhTiWEbT8frfelSgVJOKmakLPd8eQxXDOFpSFmlTP37qG4swdJljGgfPtJvtDd5pK3BwKxmyNPnFjkP/9sseTuYe3couHw4oBDr84Qxs8mOtfG5D6a7iup4wc3rcz9Ie73xQY9Dxudfixm0dqOP3DZmj7A5OPeJzLVsnUi6EITPfTD/7tw3HRAvHTGFHq8AAAAASUVORK5CYII=)
= 409.5
∴ Interest for 2nd year = Rs. 409.5
Total interest = Rs. 325+Rs. 409.5 = Rs. 734.5
Amount at second year = Principal (P) for 2nd year + Interest for 2nd year
= 6825+409.5
= 7234.5
∴ Amount at second year = Rs. 7234.5
Question 5.Prathibha borrows Rs. 47000 from a finance company to buy her first car. The rate of simple interest is 17% and she borrows the money over a 5 year period.
Find:
(a) How much amount Prathibha should repay the finance company at the end of five years.
(b) her equal monthly repayments.
Answer:(a) Principal (P) = Rs. 47000
Time period (T) = 5
Rate of interest (R) = 17%
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEUAAAAsCAMAAAAEqIWJAAAAAXNSR0IArs4c6QAAAGlQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOjpmOjqQOmaQOma2OpDbZgAAZgBmZjoAZjo6ZpDbZrb/kDoAkGY6kNv/tmYAtmY6ttv/tv//25A627aQ2////7Zm/9uQ/9u2//+2///bjFKGDwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABaklEQVRIS+WWa1fDIAyGodVanc7LmLXXVf7/j/QNpKWoO6Q69aj50OVk8JC8pFCl/qdZo8kua9U6B5Y3ISgV5Xl7oVRX5k2bPaoWhKe8URxERGjWgIJEdu0Nfohw26g5KITwhEGD4SlknsJBCSlaNqZQjUJzlK4s+je5dKXLT2RuP7JrB1lUREFxJpMEvOCyonF77kWSmNflHQrEXfyTQB2nWCOvyTXYZBXP88EDa54uicT1+wOrWFIKEqbSWZrwjSOmvD65ZCTch1nRJv5FCrqBTd6T0EGiy0w+4sgoadFf5fKFFaVzOUnXnegNSGfLI7p7f8TavdZXdexJIeMdLlU31RT9aMgPnhRy2NR8aA/UjYPe4TF7UgrGMaWiNNyWBG81hcogStEHbwWEc/Fz6Rm8n6WQLlNF8luNco7VxR3P6spv+wUFn0K808FbIQx/qMTb48uSmt2XOKHOHjAeXaw3bmrwpJhfM+4FsTwgF0c/8mMAAAAASUVORK5CYII=)
![](data:image/png;base64,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)
I = Rs. 39950
∴ Interest for 5 years is Rs. 39950
Amount at the end of 5 years = Principal + interest
Amount = 47000+39950
= 86950
∴ Amount at the end of 5 years is Rs. 86950
(b)
![](data:image/png;base64,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)
⇒ monthly repayment = ![](data:image/png;base64,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)
= 1449.17
∴ prathibha’s monthly repayment isRs. 1449.17.
Question 6.The population of Hyderabad was 68,09,000 in the year 2011. If it increases at the rate of 4.7% per annum. What will be the population at the end of the year 2015.
Answer:The population of Hyderabad (P) = 68,09,000
Time period (n) = 2015-2011 = 4
Rate of interest (R) = 4.7%
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= 6809000×1.0474
= 81821994
∴ The population of Hyderabad at the end of 2015 = 8,18,21,994
Question 7.Find Compound interest paid when a sum of Rs. 10000 is invested for 1 year and 3 months at 8
% per annum compounded annually.
Answer:Principal (P) = Rs. 10000
Rate of interest (R) = 8.5%
Time period (T) = 1year 3 months
For T = 1 year,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
I = Rs. 850
∴ Interest for 1 year is Rs. 850
Amount at the end of 1 year = Principal + interest
Amount = 10000+850
= 10850
∴ Amount at the end of 1 year is Rs. 10850
For T = 3 months = ![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEUAAAAsCAMAAAAEqIWJAAAAAXNSR0IArs4c6QAAAGlQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOjpmOjqQOmaQOma2OpDbZgAAZgBmZjoAZjo6ZpDbZrb/kDoAkGY6kNv/tmYAtmY6ttv/tv//25A627aQ2////7Zm/9uQ/9u2//+2///bjFKGDwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABaklEQVRIS+WWa1fDIAyGodVanc7LmLXXVf7/j/QNpKWoO6Q69aj50OVk8JC8pFCl/qdZo8kua9U6B5Y3ISgV5Xl7oVRX5k2bPaoWhKe8URxERGjWgIJEdu0Nfohw26g5KITwhEGD4SlknsJBCSlaNqZQjUJzlK4s+je5dKXLT2RuP7JrB1lUREFxJpMEvOCyonF77kWSmNflHQrEXfyTQB2nWCOvyTXYZBXP88EDa54uicT1+wOrWFIKEqbSWZrwjSOmvD65ZCTch1nRJv5FCrqBTd6T0EGiy0w+4sgoadFf5fKFFaVzOUnXnegNSGfLI7p7f8TavdZXdexJIeMdLlU31RT9aMgPnhRy2NR8aA/UjYPe4TF7UgrGMaWiNNyWBG81hcogStEHbwWEc/Fz6Rm8n6WQLlNF8luNco7VxR3P6spv+wUFn0K808FbIQx/qMTb48uSmt2XOKHOHjAeXaw3bmrwpJhfM+4FsTwgF0c/8mMAAAAASUVORK5CYII=)
![](data:image/png;base64,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)
I = Rs. 230.56
∴ Interest for
year is Rs. 230.56
Amount at the end of
year = Principal + interest
Amount = 10850+230.56
= 11080.56
∴ Amount at the end of
year is Rs. 11080.56
Total interest for 1.3 year = Interest for 1 year + Interest for
year
= 850+230.56
= 1080.56
∴ The compound interest paid is Rs. 1080.56
Question 8.Arif took a loan of Rs. 80,000 from a bank. If the rate of interest is 10% per annum, find the difference in amounts he would be paying after 1
years, if the interest is compounded annually and compounded half yearly.
Answer:For compounded Annually
Principal (P) = Rs. 80000
Time period (n) = 1
Rate of interest (R) = 10%
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= 80000×1.053
= 88000
∴ Amount for 1 year = Rs. 88000
Interest for remaining 6 months = ![](data:image/png;base64,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)
= 4400
∴ Amount for 1.5 years = Rs. 88000+4400 = Rs. 92400
![](data:image/png;base64,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)
= 92400-80000
∴ Compound Interest = Rs. 12400
For compounded half yearly
Principal (P) = Rs. 80000
Time period (n) = 3
Rate of interest (R) for half year = 10%×
= 5%
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= 80000×1.053
= 92610
∴ Amount = Rs. 92610
![](data:image/png;base64,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)
= 92610-80000
∴ Compound Interest = Rs. 12610
∴ the difference in amounts = amount for For compounded half yearly - amount for For compounded annually
= 92610-92400
= Rs. 210
∴ The difference in amounts is Rs. 210
Question 9.I borrowed Rs. 12000 from Prasad at 6% per annum simple interest for 2 years. Had I borrowed this sum at 6% per annum compounded annually, what extra amount would I have to pay?
Answer:Principal (P) = Rs. 12000
Rate of interest (R) = 6%
Time period (T) = 2years
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEUAAAAsCAMAAAAEqIWJAAAAAXNSR0IArs4c6QAAAGlQTFRFAAAA///b//+22///tv///9u2/9uQttv/kNv//7Zm27aQZrb/25A6ZpDbOpDbtmY6tmYAkGY6Oma2OmaQAGa2kDoAZjo6OjqQZjoAOjpmADqQADpmZgBmADo6ZgAAOgAAAABmAAA6AAAAvA5GQAAAAAF0Uk5TAEDm2GYAAAEpSURBVHja5ZbZcoMwDEXlYMJSl5DEJC1tA+j/PzIj21QwPNQKmS7pfYBrDZyRJdsA8D+lGiS9ZmAwqNccjNXmYgHKrtdmyMH0Wu16PQaHPD4ZCwAGn0wFRIHNu+agjFJgRQOiLIKiXJYUI5xR2bXJglJ2laxJw8FBJhQK5pJWWx5Mc0kvb3o9BQq0d6CoJn5OboGNqsN7PrgNNY8r7uezdSgpBa0bD79uu9r1mFnhViTz4JR6PBJF+ywqF/xCf29G37Tq7rQDolWefKHUHvGczV2s0hf0R5xq2iRtyLOL1faYhYOyoN4V9GViJ1Cg1HRzLWEnptA06N02YXcrha7sfpZC1WB3e3WrqZNT3O+H6y87CcVv8nl7ZGVR+w4RP579KsZjAjP3cLoCpRUmEtjufLwAAAAASUVORK5CYII=)
![](data:image/png;base64,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)
I = Rs. 1440
∴ Interest for 2 years is Rs. 1440
This sum to be borrowed at 6% per annum compounded annually,
Principal (P) = Rs. 12000
Rate of interest (R) = 6%
Time period (n) = 2years
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= 12000×1.062
= 13483.2
∴ Amount = Rs. 13483.2
![](data:image/png;base64,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)
= 13483.2-12000
∴ Compound Interest = Rs. 1483.2
∴ The difference in interest = 1483.2 - 1440
= Rs. 43.2
∴ The difference in interest is Rs. 43.2
Question 10.In a laboratory the count of bacteria in a certain experiment was increasing at the rate of 2.5% per hour. Find the bacteria at the end of 2 hours if the count was initially 5, 06,000
Answer:Principal (P) = 506000
Rate of interest (R) = 2.5%
Time period (n) = 2hours
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALwAAAAsCAMAAADo8SLaAAAAAXNSR0IArs4c6QAAAJZQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6Ojo6OjpmOjqQOmaQOma2OpC2OpDbZgAAZgA6ZgBmZjoAZjo6ZpCQZpC2ZpDbZrbbZrb/kDoAkGY6kLbbkNv/tmYAtmY6tmZmtpBmttuQttv/tv/btv//25A625Bm27Zm27aQ29uQ2////7Zm/9uQ/9u2//+2///bEV5TPwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAC3ElEQVRoQ+1ZiVLbMBCVQpu4zdG6hR4xYEoBt2l8/f/PdS9ZEuPBV5hETDQTs3aE9Pz8dvcZlDqPMwNvhoE60TiWD0HeURUvlNpFs9sQ0dcJgFeZ3oYLPtefwwWfBSybXRQk8YrKTZi8KwC/UGX8/ilEyRN4lWssOeENAl8nYQqHmpQqovk+ROI1SSYNNmlPifP6fjWteGRr9mm5nt9HMzEOdfJKyvK8YZ18Yv3ursa6reIjI85mNyoVzPkYYRUfekAQb3gBjNcJd8vyUuOpHXXS33zJphkAxw+O9NuINpz3qWKON8wZcrF+yMaDF8gO+OrrI+km13r7J9IbRQfc6FLrFciMnkwRgT1tpqg7fFfwUbTkF4NHb8gRP/QJ4Jl6B3y2kPWKaHkLFnp5A6KCOUX0U5UJ7kSnOXprmQLRQOaLqBHHFPAkPuBxAR+UIWqOl6ZjgRKiKOU2YYAKeDPlGfiUXttwuHIivnfYaZzpU8AzKDuK1V4eqoAneFtVxXhrdKSdLXh7rUUp3iX2hhvUpL0nB/zzW24YaA0oP/3CmNFEVEcbeDZI48EbohzE05j3wFdfMAVcTYxi/gXZ0LM4mGw88DmdUUH2mefW1ab5IbIxzB8MvKt5KWFVDLoR+ilhUemQz6XcwWZfXmG18af86upT7A1xuNXG7xBDmpQkosmrWGsguIIfF78jKPRQguSg1F+IMdkUVPXZ939Q6OlbnAz3Bte6WiPmqzxmU+fra1hCv/th83oQ+F59vauMDP9eOmz3LxrrU19zi4Ri3kSNKehe5qAzjLfpWLSxPphy3CJtpI5EPGIQV/kSfGt9bHl2CrW4yoOy2m+xnn5e2kCKpFPCN5Hx8/22O8osBs+FuornexsdBc6wTV3wCJzBv9oL0zBwXbPfDHjUvJFNEH9/8hMWuqEkLESnPwQ8/V+B3IiNAgDP1scvNEHkq2N9oNfqNTkrG50+9WeEJ8/Af94CXl07fmiqAAAAAElFTkSuQmCC)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKcAAAAsCAMAAAA3v1jFAAAAAXNSR0IArs4c6QAAAI1QTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6Ojo6OjpmOjqQOmaQOma2OpC2OpDbZgAAZgA6ZjoAZjo6ZpDbZrbbZrb/kDoAkDo6kGY6kLaQkLbbkNv/tmYAtmY6tpBmttv/tv//25A625Bm27Zm27aQ29u229v/2////7Zm/9uQ/9u2//+2///bJvWZbgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACq0lEQVRYR+2Ya1fbMAyG7cGoxyiswFjGWDYI7dak9f//eZMsx3Jy1NxKznF38IcgjGs/yLq8qVLv4//2wOvP9P4/u7nT+mMNVhkN40OCnLl+ULvV2Qt5sDLf0nOlI8oX8Ci0x0uX08GWJ8KZp3/vzaiszGfDWZVYqNrsS01kv0NWZSnmu1I2w1SKRmUCd0oezRfbJs5+1QJPgra4AMzSezDHn0n6s/oEzccCn/NiDqG5y+rsT8KPHiLHRqm159zdg718bgL+gc56nRKzzLK/fVLr3hIwWbvY31e+aU90RRH51UXHgRFpF/uo9ZW/DfvLYOQrnpMsqDY3lMab+6nqp7oMoqToqFSsCWx2sa2juzTXf/F4npMs+DPtvLvTzayw2XBFFLy47gpP5iwxOkgrlOaB3M9zkqVKoquWz8V0TuVqFsipzixiTicTXN3gEsxzkhX1mGM4yaElYJaHbyFw4sUiIjyDAOM5yYr17jGcLnr2KyxcyOlrWEvxB+1CJO6Zn/3AYral39xTsigqaBzDSSq6ZwTtEpNoyOIN6IRJnG1/UIk/NBAvpwDtH9hr65tdeAs/3Z7DwOW52InH+bPBKd+7+yeo61Ie1cSOIsyJ1pvd+wB/snZxr1kuhegFAW+D5yTrzTgHxCdrF0x1utTKgFhcIzHPSVb03lg0W/OYOu/usHdE2gW6il66iK7wW4EntHhOsOr6aR/xi4Pzr3zYKM6utt7LP2iB70f9a+v2L4oE34/6d5m8Ino369ojtH9RJMzvTmwBXi91YXL7l0RCpJcm+6v/gwP1py+vgkiI9Wf/cXOvIE5RJMx99Kj9Y86mXBi1zeyLT5GzJRJm99GYA5p5BO2HhcOYbWZf6zklkTD72WMO8O1fEgljtpl3bdT+Jbkw7+Hvu5+GB/4BPkVgvmQc8sAAAAAASUVORK5CYII=)
= 506000×1.0252
= 531616.25
∴ The number of the bacteria at the end of 2 hours is 531616(approximately)
Question 11.Kamala borrowed Rs. 26400 from a bank to buy a scooter at a rate of 15% per annum compounded yearly. What amount will she pay at the end of 2 years and 4 months to clear the loan?
Answer:Principal (P) = 26400
Rate of interest (R) = 15%
Time period (T) = 2 years and 4 months
Amount for 2 years,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= 26400×1.152
= Rs. 34914
∴ Amount for 2 year = Rs. 34914
Interest for remaining 4 months = ![](data:image/png;base64,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)
= 1745.70
∴ Total amount for 2 years and 4 months = Rs. 34914 + 1745.70
= Rs. 36659.70
∴ The total amount to clear the loan is Rs. 36659.70
Question 12.Bharathi borrows an amount of Rs. 12500 at 12% per annum for 3 years at a simple interest and Madhuri borrows the same amount for the same time period at 10% per annum, compounded annually. Who pays more interest and by how much?
Answer:Principal (P) = Rs. 12500
Rate of interest (R) = 12%
Time period (T) = 3years
Interest paid by bharathi,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
I = Rs. 4500
∴ Interest paid by bharathi is Rs. 4500
Amount paid by madhuri,
Principal (P) = Rs. 12500
Rate of interest (R) = 10%
Time period (n) = 3years
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= 12500×1.13
= Rs. 16637.5
∴ Amount paid by madhuri isRs. 16637.5
Interest = A-P
= Rs. 16637.5 – 12500
= Rs. 4137.5
∴ Interest paid by madhuri is Rs. 4137.5
On comparing the interests paid by bharathi and madhuri,
4500-4137.5 = 362.5
∴ Bharathi paid Rs.362.5 more than by madhuri.
Question 13.Machinery worth Rs. 10000 depreciated by 5%. Find its value after 1 year.
Answer:Principal (P) = 10000
Depreciation (R) = 5%
Time period (n) = 1 year
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= Rs. 9500
∴The value of machinery after 1 year is Rs. 9500
Question 14.Find the population of a city after 2 years which is at present 12 lakh, if the rate of increase is 4%.
Answer:Present population (P) = 12 lakh
Rate of interest (R) = 4%
Time period (n) = 2years
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= 1200000×1.042
= 1297920
∴ The population of a city after 2 years is 1297920
Question 15.Calculate compound interest on Rs. 1000 over a period of 1 year at 10% per annum, if interest is compounded quarterly?
Answer:Principal (P) = 1000
Rate of interest (R) = 10%
Time period (n) = 1 year
For quarterly, n = 4
Rate of interest (R) for quarterly = ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
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= 1000![](data:image/png;base64,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)
= 1103.81
∴ Amount = Rs. 1103.81
Interest = A-P
= 1103.81-1000
= 103.81
∴ compound interest = Rs. 103.81
Sudhakar borrows Rs. 15000 from a bank to renovate his house. He borrows the money at 9% p.a. simple interest over 8 years. What are his monthly repayments?
Answer:
Principal (P) = Rs. 15000
Time period (T) = 8
Rate of interest (R) = 9%
I = Rs. 10800
∴ Interest for 8 years is Rs. 10800
Amount to be paid at the end of 8 years = Principal + interest
Amount = 15000+10800
= 25800
∴ Amount to be paid at the end of 8 years is Rs. 25800
⇒ monthly repayment =
= 268.75
∴ Sudhakar pays Rs. 268.75 monthly.
Question 2.
A TV was bought at a price of Rs. 21000. After 1 year the value of the TV was depreciated by 5% (Depreciation means reduction of the value due to use and age of the item). Find the value of the TV after 1 year.
Answer:
Cost price of TV = Rs. 21000
Depreciation = 5%
Depreciation after 1 year = 5% of 21000
∴ Depreciation after 1 year = Rs. 1050
Value of TV after 1 year = cost price – depreciation
= 21000 – 1050
= Rs. 19950
∴The value of TV after 1 year is Rs. 19,950
Question 3.
Find the amount and the compound interest on Rs. 8000 at 5% per annum, for 2 years compounded annually.
Answer:
Principal (P) = Rs. 8000
Time period (n) = 2
Rate of interest (R) = 5%
= 8000×1.052
= 8820
∴ Amount = Rs. 8820
= (8000×1.052)-8000
= 8820-8000
= 820
∴ Compound Interest = Rs. 820
Question 4.
Find the amount and the compound interest on Rs. 6500 for 2 years, compounded annually, the rate of interest being 5% per annum during the first year and 6% per annum during the second year.
Answer:
Principal (P) for 1st year = Rs. 6500
Rate of interest (R) for first year = 5%
Interest on first year = 5% of 6500
=
= 325
∴ Interest for 1st year = Rs. 325
Principal (P) for second year = Principal (P) for 1st year + Interest for 1st year
Principal (P) for second year = Rs. 6500 + Rs. 325 = Rs. 6825
Rate of interest (R) for second year = 6%
Interest on second year = 6% of 6825
=
= 409.5
∴ Interest for 2nd year = Rs. 409.5
Total interest = Rs. 325+Rs. 409.5 = Rs. 734.5
Amount at second year = Principal (P) for 2nd year + Interest for 2nd year
= 6825+409.5
= 7234.5
∴ Amount at second year = Rs. 7234.5
Question 5.
Prathibha borrows Rs. 47000 from a finance company to buy her first car. The rate of simple interest is 17% and she borrows the money over a 5 year period.
Find:
(a) How much amount Prathibha should repay the finance company at the end of five years.
(b) her equal monthly repayments.
Answer:
(a) Principal (P) = Rs. 47000
Time period (T) = 5
Rate of interest (R) = 17%
I = Rs. 39950
∴ Interest for 5 years is Rs. 39950
Amount at the end of 5 years = Principal + interest
Amount = 47000+39950
= 86950
∴ Amount at the end of 5 years is Rs. 86950
(b)
⇒ monthly repayment =
= 1449.17
∴ prathibha’s monthly repayment isRs. 1449.17.
Question 6.
The population of Hyderabad was 68,09,000 in the year 2011. If it increases at the rate of 4.7% per annum. What will be the population at the end of the year 2015.
Answer:
The population of Hyderabad (P) = 68,09,000
Time period (n) = 2015-2011 = 4
Rate of interest (R) = 4.7%
= 6809000×1.0474
= 81821994
∴ The population of Hyderabad at the end of 2015 = 8,18,21,994
Question 7.
Find Compound interest paid when a sum of Rs. 10000 is invested for 1 year and 3 months at 8 % per annum compounded annually.
Answer:
Principal (P) = Rs. 10000
Rate of interest (R) = 8.5%
Time period (T) = 1year 3 months
For T = 1 year,
I = Rs. 850
∴ Interest for 1 year is Rs. 850
Amount at the end of 1 year = Principal + interest
Amount = 10000+850
= 10850
∴ Amount at the end of 1 year is Rs. 10850
For T = 3 months =
I = Rs. 230.56
∴ Interest for year is Rs. 230.56
Amount at the end of year = Principal + interest
Amount = 10850+230.56
= 11080.56
∴ Amount at the end of year is Rs. 11080.56
Total interest for 1.3 year = Interest for 1 year + Interest for year
= 850+230.56
= 1080.56
∴ The compound interest paid is Rs. 1080.56
Question 8.
Arif took a loan of Rs. 80,000 from a bank. If the rate of interest is 10% per annum, find the difference in amounts he would be paying after 1years, if the interest is compounded annually and compounded half yearly.
Answer:
For compounded Annually
Principal (P) = Rs. 80000
Time period (n) = 1
Rate of interest (R) = 10%
= 80000×1.053
= 88000
∴ Amount for 1 year = Rs. 88000
Interest for remaining 6 months =
= 4400
∴ Amount for 1.5 years = Rs. 88000+4400 = Rs. 92400
= 92400-80000
∴ Compound Interest = Rs. 12400
For compounded half yearly
Principal (P) = Rs. 80000
Time period (n) = 3
Rate of interest (R) for half year = 10%× = 5%
= 80000×1.053
= 92610
∴ Amount = Rs. 92610
= 92610-80000
∴ Compound Interest = Rs. 12610
∴ the difference in amounts = amount for For compounded half yearly - amount for For compounded annually
= 92610-92400
= Rs. 210
∴ The difference in amounts is Rs. 210
Question 9.
I borrowed Rs. 12000 from Prasad at 6% per annum simple interest for 2 years. Had I borrowed this sum at 6% per annum compounded annually, what extra amount would I have to pay?
Answer:
Principal (P) = Rs. 12000
Rate of interest (R) = 6%
Time period (T) = 2years
I = Rs. 1440
∴ Interest for 2 years is Rs. 1440
This sum to be borrowed at 6% per annum compounded annually,
Principal (P) = Rs. 12000
Rate of interest (R) = 6%
Time period (n) = 2years
= 12000×1.062
= 13483.2
∴ Amount = Rs. 13483.2
= 13483.2-12000
∴ Compound Interest = Rs. 1483.2
∴ The difference in interest = 1483.2 - 1440
= Rs. 43.2
∴ The difference in interest is Rs. 43.2
Question 10.
In a laboratory the count of bacteria in a certain experiment was increasing at the rate of 2.5% per hour. Find the bacteria at the end of 2 hours if the count was initially 5, 06,000
Answer:
Principal (P) = 506000
Rate of interest (R) = 2.5%
Time period (n) = 2hours
= 506000×1.0252
= 531616.25
∴ The number of the bacteria at the end of 2 hours is 531616(approximately)
Question 11.
Kamala borrowed Rs. 26400 from a bank to buy a scooter at a rate of 15% per annum compounded yearly. What amount will she pay at the end of 2 years and 4 months to clear the loan?
Answer:
Principal (P) = 26400
Rate of interest (R) = 15%
Time period (T) = 2 years and 4 months
Amount for 2 years,
= 26400×1.152
= Rs. 34914
∴ Amount for 2 year = Rs. 34914
Interest for remaining 4 months =
= 1745.70
∴ Total amount for 2 years and 4 months = Rs. 34914 + 1745.70
= Rs. 36659.70
∴ The total amount to clear the loan is Rs. 36659.70
Question 12.
Bharathi borrows an amount of Rs. 12500 at 12% per annum for 3 years at a simple interest and Madhuri borrows the same amount for the same time period at 10% per annum, compounded annually. Who pays more interest and by how much?
Answer:
Principal (P) = Rs. 12500
Rate of interest (R) = 12%
Time period (T) = 3years
Interest paid by bharathi,
I = Rs. 4500
∴ Interest paid by bharathi is Rs. 4500
Amount paid by madhuri,
Principal (P) = Rs. 12500
Rate of interest (R) = 10%
Time period (n) = 3years
= 12500×1.13
= Rs. 16637.5
∴ Amount paid by madhuri isRs. 16637.5
Interest = A-P
= Rs. 16637.5 – 12500
= Rs. 4137.5
∴ Interest paid by madhuri is Rs. 4137.5
On comparing the interests paid by bharathi and madhuri,
4500-4137.5 = 362.5
∴ Bharathi paid Rs.362.5 more than by madhuri.
Question 13.
Machinery worth Rs. 10000 depreciated by 5%. Find its value after 1 year.
Answer:
Principal (P) = 10000
Depreciation (R) = 5%
Time period (n) = 1 year
= Rs. 9500
∴The value of machinery after 1 year is Rs. 9500
Question 14.
Find the population of a city after 2 years which is at present 12 lakh, if the rate of increase is 4%.
Answer:
Present population (P) = 12 lakh
Rate of interest (R) = 4%
Time period (n) = 2years
= 1200000×1.042
= 1297920
∴ The population of a city after 2 years is 1297920
Question 15.
Calculate compound interest on Rs. 1000 over a period of 1 year at 10% per annum, if interest is compounded quarterly?
Answer:
Principal (P) = 1000
Rate of interest (R) = 10%
Time period (n) = 1 year
For quarterly, n = 4
Rate of interest (R) for quarterly =
= 1000
= 1103.81
∴ Amount = Rs. 1103.81
Interest = A-P
= 1103.81-1000
= 103.81
∴ compound interest = Rs. 103.81