Variation
Class 8th Mathematics (new) MHB Solution
Class 8th Mathematics (new) MHB Solution
Practice Set 7.1- Write the following statements using the symbol of variation.(1) Circumference (c) of a…
- Complete the following table considering that the cost of apples and their number are…
- If m proportional n and whenm=154, n=7. Find the value of m, when n=14.…
- If n varies directly as m, complete the following table.m356.5. . .1.25n1220. . .28. .…
- y varies directly as the square root of x. When x = 16, y = 24. Find the constant of…
- The total remuneration paid to laborers, employed to harvest soybeans is indirect…
Practice Set 7.2- The information about numbers of workers and the number of days to complete work is…
- Find constant of variation and write equation of variation for every example given…
- The boxes are to be filled with apples in a heap. If 24 apples are put in a box then 27…
- Write the following statements using the symbol of variation.(1) The wavelength of…
- x alpha {1}/{ root {y} } and when x = 40 then y = 16. If x = 10, find y.…
- X varies inversely as y, when x = 15 then y = 10, if x = 20 then y =?…
Practice Set 7.3- Which of the following statements is of inverse variation?(1) The number of workers on…
- If 15 workers can build a wall in 48 hours, how many workers will be required to do the…
- 120 bags of half liter milk can be filled by a machine within 3 minutes find the time…
- A car with a speed of 60 km/hr takes 8 hours to travel some distance. What should be…
- Write the following statements using the symbol of variation.(1) Circumference (c) of a…
- Complete the following table considering that the cost of apples and their number are…
- If m proportional n and whenm=154, n=7. Find the value of m, when n=14.…
- If n varies directly as m, complete the following table.m356.5. . .1.25n1220. . .28. .…
- y varies directly as the square root of x. When x = 16, y = 24. Find the constant of…
- The total remuneration paid to laborers, employed to harvest soybeans is indirect…
- The information about numbers of workers and the number of days to complete work is…
- Find constant of variation and write equation of variation for every example given…
- The boxes are to be filled with apples in a heap. If 24 apples are put in a box then 27…
- Write the following statements using the symbol of variation.(1) The wavelength of…
- x alpha {1}/{ root {y} } and when x = 40 then y = 16. If x = 10, find y.…
- X varies inversely as y, when x = 15 then y = 10, if x = 20 then y =?…
- Which of the following statements is of inverse variation?(1) The number of workers on…
- If 15 workers can build a wall in 48 hours, how many workers will be required to do the…
- 120 bags of half liter milk can be filled by a machine within 3 minutes find the time…
- A car with a speed of 60 km/hr takes 8 hours to travel some distance. What should be…
Practice Set 7.1
Question 1.Write the following statements using the symbol of variation.
(1) Circumference (c) of a circle is directly proportional to its radius (r).
(2) Consumption of petrol (I) in a car and distance traveled by that car (D) are in direct variation.
Answer:(1) Circumference
and radius![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB4AAAAVBAMAAACj2UNSAAAAAXNSR0IArs4c6QAAAC1QTFRFAAAAAAAAAAA6OgAAOgA6OjpmOpDbZrbbZrb/kNv/tmYA25Bm27aQ/7Zm/9uQ2su55wAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAOElEQVQoU2NgGDzgosRmTWTX8JnWeAL5XIJAIDSBgYHPDNWtfBZY+Qj12OXhmnglUPU/FkygODAAODwHg6fTUGoAAAAASUVORK5CYII=)
Therefore,
or
, where ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGMAAAAVCAMAAABlnqB7AAAAAXNSR0IArs4c6QAAAIRQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OjoAOjpmOjqQOmaQOma2OpDbZgAAZjoAZjo6ZmY6ZrbbZrb/kDoAkDo6kGYAkLyQkLbbkNv/tmYAtmY6tmZmttvbttv/tv//25A625Bm27Zm27aQ2/+22////7Zm/9uQ/9u2//+2///bBr/LigAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABZ0lEQVRIS+1TXVeCQBDdQZTSAEu0EixNQ3D////r3lkCPLE91SnPcR6WPczHnbl31pir/SsGdhKsf72h46VgVDceMpzjR+bwFnEOnjuR8NWrSjUXCTJj+J0h7CiSvUUSI6FewRWXhcBGW7u/Ff7uAtThMOxyUvohooWp08xU/C5HW4BFU/aVIW9c2sdx6chgFZvz1gY0LNF9nH1C5ARWa1chRw1aPsFRRRzIHYk5pQkuSO64Og/oMPYtxMAwWgfmvq4qMfRWyPSFziEMDWj0QM9Np4N0nWOAjz6GgQIh2HOl7OE+glb9gFbzKiINjpAvXH07BzIOTG716JHZn4N6ENxj2jmbhL59PViCUhjqpRh6dHqccYX6ug0e28nC2A0bSbBXBNKWqLmu2lzZS8zmCUf9QK3aAHVwl4O1XQoK+AxvIXyGcw+yY50FpJ9SpNQrXO+4dgVfEF5D/J5K1gWow1v46vgTBj4AnAQlt2GeEhwAAAAASUVORK5CYII=)
(2) Consumption of petrol in a car ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABgAAAAVBAMAAACuxzMVAAAAAXNSR0IArs4c6QAAAB5QTFRFAAAAAAAAAAA6AGa2ZgAAkDoAkNv/tmYA//+2///bpNS76gAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAKklEQVQoU2NgoBqYKmiAMIvDGclczmB8HHZBIBBKYGCgWBmKpSjOId6TADTkBp3RQnG7AAAAAElFTkSuQmCC)
Distance traveled by that car ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB4AAAAVCAMAAABmKa5TAAAAAXNSR0IArs4c6QAAAD9QTFRFAAAAAAAAAAA6ADqQAGa2OgAAOjpmOmaQOpDbZgAAZrb/kDoAkNv/tmYAttvbttv/2////9uQ/9u2//+2///bmm4Q9QAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAZklEQVQoU9WSzRKAIAiEV8vK6M/k/Z81NTol47FpLxy+YWEZgD+JySTZYVOWjr4HTjJTnTMlDCa7VPmNEVwpLwmOvjuANS9S9JgJZspY7W7ghnlw9WQye1WCyVnsrOQqMcb940+4AEywA6ZVxw4kAAAAAElFTkSuQmCC)
OR ![](data:image/png;base64,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)
Question 2.Complete the following table considering that the cost of apples and their number are in direct variation.
![](data:image/png;base64,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)
Answer:Since, cost of apples and their number are in direct variation it means that as the number of apple increases, the cost also increases and as the number of apple decreases, the cost also decreases.
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)
![](data:image/png;base64,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)
EXPLANATION:
• When no. of apples is 1 [
]
Cost of apple is 8 [
]
Now, when no. of apples become 4 times then the cost of apples will also become 4 times because they are inversely proportion.
![](data:image/png;base64,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)
![](data:image/png;base64,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)
• When Cost of apple is 8 [
]
No. of apples is 4 [
]
Now, the cost of apples becomes
times.
![](data:image/png;base64,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)
![](data:image/png;base64,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)
∴ No. of apples will also become
times.
![](data:image/png;base64,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)
![](data:image/png;base64,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)
• When no. of apples is 7 [
]
Cost of apple is 56[
]
Now, no. of apples becomes
times.
![](data:image/png;base64,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)
![](data:image/png;base64,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)
∴ Cost of apples will also become
times.
![](data:image/png;base64,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)
![](data:image/png;base64,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)
• When Cost of apple is 96 [
]
No. of apples is 12 [
]
Now, the cost of apples becomes
times.
![](data:image/png;base64,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)
![](data:image/png;base64,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)
∴ No. of apples will also become
times.
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 3.If
and when
m=154, n=7. Find the value of m, when n=14.
Answer:GIVEN:
m∝n
m=154
n=7
TO FIND: Value of m, when n=14
PROOF:
m∝n
That is, 154∝7
It means that as the value of m increases, the value of n also increases.
When n=14, n becomes 2 times of its original value.
∵ m∝n
∴ m will also get double.
m=154×2
m=308
m∝n
308∝14
∴ Value of m is 308.
Question 4.If n varies directly as m, complete the following table.
![](data:image/png;base64,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)
Answer:It is given that
. It means that as the value of n increases, the value of m also increases and if the value of n decreases, the value of n also decreases.
![](data:image/png;base64,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)
• When m =3
n =12
Now, when m becomes
times. ∴ n will also become
times.
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
• When ![](data:image/png;base64,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)
![](data:image/png;base64,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)
Now, when m becomes 1.3 times.
![](data:image/png;base64,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)
![](data:image/png;base64,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)
∴ n will also become 1.3 times.
![](data:image/png;base64,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)
![](data:image/png;base64,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)
• When ![](data:image/png;base64,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)
![](data:image/png;base64,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)
Now, when m becomes
times.
![](data:image/png;base64,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)
∴ m will also become
times.
![](data:image/png;base64,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)
• When m =7
n = 28
Now, when m becomes
times.
![](data:image/png;base64,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)
∴ n will also become
times.
![](data:image/png;base64,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)
Question 5.y varies directly as the square root of x. When x = 16, y = 24. Find the constant of variation and equation of variation.
Answer:It is given that y varies directly as the square root of x.
![](data:image/png;base64,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)
![](data:image/png;base64,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)
(k is a constant)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
∴ Required constant ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABwAAAAVCAMAAABi3H5uAAAAAXNSR0IArs4c6QAAAF1QTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOma2OpC2OpDbZgAAZjoAZrbbZrb/kDoAkLaQkLbbkNv/tmYAtmY6tv//25A627Zm27aQ29v/2////7Zm/9uQ//+2///bIdq9bgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAb0lEQVQoU2NgGBpAToSdVQqHU6XZOSRx+UKanRenB2W52XB7XpqRDyYpzAgDTEIQMWFmAR5GRg6sDpLjZ+SUYpBg58Jmthw/2BfCIBLDWKikGLMoNq3CYGGwTkwgw84mxSCOcDKqChmgY1kEByaiAX6PBFCt94TCAAAAAElFTkSuQmCC)
Equation: ![](data:image/png;base64,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)
Question 6.The total remuneration paid to laborers, employed to harvest soybeans is indirect variation with the number of laborers. If remuneration of 4 laborers is Rs1000, find the remuneration of 17 laborers.
Answer:It is given that the total remuneration paid to laborers, employed to harvest soybeans is direct variation with the no. of laborers.
![](data:image/png;base64,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)
Remuneration of 4 labourers ![](data:image/png;base64,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)
Remuneration of 1 labour ![](data:image/png;base64,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)
Remuneration of 17 labourers![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
ALTERNATIVE METHOD
Total remuneration of 4 laborers is Rs 1000.
![](data:image/png;base64,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)
Remuneration of 17 laborers
To get the number of laborers to be 17, the present number of laborers will be multiplied by ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAeCAMAAADEgrRGAAAAAXNSR0IArs4c6QAAAF1QTFRFAAAAAAAAAABmADqQAGaQAGa2OgAAOjoAOmZmOma2OpDbZjoAZjpmZrbbZrb/kDoAkDo6kDqQkGaQkNv/tmYAtmY6tv//25A625Bm29uQ2////7Zm/9uQ//+2///b6UDxpgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAfElEQVQoU62RyQ6AIAxEwX0HN1DR/v9nSisSPBgvzgVepp0mLWOfgjm1NSC4lf0tRU3cbwzkiN0aGWVKem52tmfj6px/2zAlG3VftsY5lR1whf8tTA/0d/xb3p51oQUyf7BuRcimhJCPRoFoB9qSXxGPPdN5HnlszSKFpSd9swWnNUUFAwAAAABJRU5ErkJggg==)
Since total remuneration is in direct variation with the number of laborers total remuneration will also get
times.
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHEAAAAVCAMAAABGxfGuAAAAAXNSR0IArs4c6QAAAH5QTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OgBmOjpmOjqQOmaQOpDbZgAAZgA6ZjoAZjo6ZmZmZpBmZpDbZrbbZrb/kDoAkDo6kGY6kNv/tmYAtmY6ttuQttv/tv//25A625Bm27aQ2////7Zm/9uQ/9u2//+2///bJrjQFQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABkUlEQVRIS+1U3VqDMAxtp7LqBripG9uKyAaFvv8LmqRlbWGAN174uVzw0yY5JydpGbvb/1TgfPq9ussFJteXDedP+KUEBzOLR87XxY+gL1uiWGIs51E1EaQEJZd8x5r04QsR99ZdZ1HVZLg2Z82GGzeJsS7Drbg2fTOIS2IIAc6/xp0a15ydBU+g+DwoQ8VF6RHzv4eYMqG8xii7Q5SYpU2Ry9UjKnSeMBn1tfZQ2hQ4jVq9rjxEgrgioqiI6DVFZ0BJH96HSnuIZjCgT525kiDd64k5RIOlxErQDBlE87SG/gOhac8h6swXpVerzqB+QCypVfSHJcAMZcBrFFEugtb2EHuNDyHrrm7MEHBTIrGIQR9JVbX6fAH1Q3M1SqvJbVUxqlNVLr1DRDh2cvw5KKOiOewZvMYQkeuMWcQSqdXgLTGC4uiw9ETK+WIH++Hp8PtINKfNjJZ6xllBNAn/5tzjmAaDM5HIDijEzJdobjSrOrg3W+huTKrBVcLjqQvLUtBHvBkfP7wezdV53/8bCnwDPnwiWSddRjEAAAAASUVORK5CYII=)
∴ Remuneration of 17 labourers![](data:image/png;base64,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)
Write the following statements using the symbol of variation.
(1) Circumference (c) of a circle is directly proportional to its radius (r).
(2) Consumption of petrol (I) in a car and distance traveled by that car (D) are in direct variation.
Answer:
(1) Circumference and radius
Therefore, or
, where
(2) Consumption of petrol in a car
Distance traveled by that car
OR
Question 2.
Complete the following table considering that the cost of apples and their number are in direct variation.
Answer:
Since, cost of apples and their number are in direct variation it means that as the number of apple increases, the cost also increases and as the number of apple decreases, the cost also decreases.
EXPLANATION:
• When no. of apples is 1 []
Cost of apple is 8 []
Now, when no. of apples become 4 times then the cost of apples will also become 4 times because they are inversely proportion.
• When Cost of apple is 8 []
No. of apples is 4 []
Now, the cost of apples becomes times.
∴ No. of apples will also become times.
• When no. of apples is 7 []
Cost of apple is 56[]
Now, no. of apples becomes times.
∴ Cost of apples will also become times.
• When Cost of apple is 96 []
No. of apples is 12 []
Now, the cost of apples becomes times.
∴ No. of apples will also become times.
Question 3.
If and when
m=154, n=7. Find the value of m, when n=14.
Answer:
GIVEN:
m∝n
m=154
n=7
TO FIND: Value of m, when n=14
PROOF:
m∝n
That is, 154∝7
It means that as the value of m increases, the value of n also increases.
When n=14, n becomes 2 times of its original value.
∵ m∝n
∴ m will also get double.
m=154×2
m=308
m∝n
308∝14
∴ Value of m is 308.
Question 4.
If n varies directly as m, complete the following table.
Answer:
It is given that . It means that as the value of n increases, the value of m also increases and if the value of n decreases, the value of n also decreases.
• When m =3
n =12
Now, when m becomes times. ∴ n will also become
times.
• When
Now, when m becomes 1.3 times.
∴ n will also become 1.3 times.
• When
Now, when m becomes times.
∴ m will also become times.
• When m =7
n = 28
Now, when m becomes times.
∴ n will also become times.
Question 5.
y varies directly as the square root of x. When x = 16, y = 24. Find the constant of variation and equation of variation.
Answer:
It is given that y varies directly as the square root of x.
(k is a constant)
∴ Required constant
Equation:
Question 6.
The total remuneration paid to laborers, employed to harvest soybeans is indirect variation with the number of laborers. If remuneration of 4 laborers is Rs1000, find the remuneration of 17 laborers.
Answer:
It is given that the total remuneration paid to laborers, employed to harvest soybeans is direct variation with the no. of laborers.
Remuneration of 4 labourers
Remuneration of 1 labour
Remuneration of 17 labourers
ALTERNATIVE METHOD
Total remuneration of 4 laborers is Rs 1000.
Remuneration of 17 laborers
To get the number of laborers to be 17, the present number of laborers will be multiplied by
Since total remuneration is in direct variation with the number of laborers total remuneration will also get times.
∴ Remuneration of 17 labourers
Practice Set 7.2
Question 1.The information about numbers of workers and the number of days to complete work is given in the following table. Complete the table.
![](data:image/png;base64,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)
Answer:Number of workers and the number of days to complete a work will be inversely proportional because if the number of workers increases the number of days to complete the work will reduce.
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)
When the number of workers![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACYAAAAVCAMAAAAdDWyfAAAAAXNSR0IArs4c6QAAAGBQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOjoAOjqQOmaQOma2OpDbZgAAZjoAZrb/kDoAkGY6kLbbkNv/tmYAttv/tv//25A627Zm27aQ2////7Zm/9uQ/9u2//+2///bgMkJeQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAm0lEQVQ4T92QzRLCIAyESauitVWw+FvTvP9bmoWRi+l4dfwOGSYsbDbO/SVy2xKtRmSTSLQ72ylTc3IcGtVJWD84tBdTlzbavtLRuQnaCaclEv7IZR7wzIRjpxPBEzLURG/gkJkHok6viqxUm7tXv+8yHbyvppjNMIXB0/c1gp4+kYB2XkPZir0QwWa5hlxMwNET7XM6PpTMv8wLI7oJoJeWO/oAAAAASUVORK5CYII=)
Number of days ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABwAAAAVCAMAAABi3H5uAAAAAXNSR0IArs4c6QAAAF1QTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOma2OpC2OpDbZgAAZjoAZrbbZrb/kDoAkLaQkLbbkNv/tmYAtmY6tv//25A627Zm27aQ29v/2////7Zm/9uQ//+2///bIdq9bgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAb0lEQVQoU2NgGBpAToSdVQqHU6XZOSRx+UKanRenB2W52XB7XpqRDyYpzAgDTEIQMWFmAR5GRg6sDpLjZ+SUYpBg58Jmthw/2BfCIBLDWKikGLMoNq3CYGGwTkwgw84mxSCOcDKqChmgY1kEByaiAX6PBFCt94TCAAAAAElFTkSuQmCC)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADMAAAApCAMAAACvMuHlAAAAAXNSR0IArs4c6QAAAIRQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOjoAOjqQOmaQOma2OpC2OpDbZgAAZjoAZjo6ZpDbZrbbZrb/kDoAkGY6kLaQkLbbkNu2kNv/tmYAtmY6tmZmtrZmttv/tv//25A627Zm27aQ27a229v/2////7Zm/9uQ/9u2//+2///bAB8plQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABUElEQVRIS+1VXVODMBDMgbWpVMDWYC3VWrCEkP///7zLRdRpxknGGR8c9yF0QvY+9pZUiL+C/m6f2IqpIX9J44zF8ZTKwQz/nF/UIEv0gW0kAFxt0pzwo9O2WwEsXJ22Abg5RkRrs50wipqz6nowKsaG7ZLMB/dCaCJq+hWFlqK7ZaooBmGsseSpKsMBTFNgF1QacWglityILn8OT2SqAAo8xxxeES0+rVq9Z73I1kss6yuHi3J9MnCeHn5DQznXxpGZo33SUE+jxBNeA26aOW7rAla5eFQDC+6rsQrzTXVQAkvjNLNkswTilO3t02NVvgYyGbLr2mmFF5hT0AGNhI46+FehhuL27EF+I0owhpbrc1zw+ZSW20TGJyfGM+Md/xGzzR9QV1Y4ElbB7SB6Mkw0/LTJ7tHwnLS/E/ZrUh78cJeD6KKvC24ALwhY7IR4A426G63Ej9e4AAAAAElFTkSuQmCC)
[k = constant]
- (1)
The value of k will remain the same in all the cases
When the number of days ![](data:image/png;base64,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)
Number of workers ![](data:image/png;base64,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)
Number of workers
(k=constant)
Number of workers
(from 1)
Number of workers![](data:image/png;base64,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)
∴ Number of workers
15 when the number of days is 12
When the number of workers![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACYAAAAVCAMAAAAdDWyfAAAAAXNSR0IArs4c6QAAAFpQTFRFAAAAAAAAAAA6AABmADo6ADqQAGa2OgAAOjqQOmaQOpDbZgAAZjoAZjo6ZpDbZrb/kDoAkGY6kNv/tmYAttv/tv//25A627aQ2////7Zm/9uQ/9u2//+2///bx4OD6QAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAgklEQVQ4T92SSQ6AIAxFqfMsijNy/2tKKa4UTFwZ/6Ih4YXyCoz9NXPdGzXVAWSDw1JWEI6G4vEiOa0v2fJhoq010Ieu0LqGZjGB9F4mfgx7IoZVwBnsYEOnEUb1Ni8wupunKbMKxYPphLPwDYR0UNJpoLpUy0eN5vR7QO7y/MhPPQA5XwgphoPyrQAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Number of days
(from 1)
Number of days ![](data:image/png;base64,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)
∴When the number of workers=10, number of days is 18
When the number of days![](data:image/png;base64,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)
Number of workers ![](data:image/png;base64,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)
Number of workers ![](data:image/png;base64,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)
Number of workers
(from1)
Number of workers![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACAAAAAVCAMAAAAQExzYAAAAAXNSR0IArs4c6QAAAEtQTFRFAAAAAAAAAAA6AABmADpmAGa2OgAAOjpmOmaQOpDbZgAAZjo6ZrbbZrb/kDoAkDo6kNv/tmYAttv/tv//25Bm/9uQ/9u2//+2///bgVTi6AAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAZUlEQVQoU2NgGOxARACnC0XZGIGACZ8CXvzeE2WjsgJBkIvAAOYsUTZ2NkYW3G5kkODnYRDjw+MLsBdE2TihXsG0AiwhzsWK06+CIL0IEzDVCQKtF+NjFsZpghg30EscQoMjsQAAwaIDF3vfxFUAAAAASUVORK5CYII=)
∴When the number of days is 36, the number of workers will be 5
Question 2.Find constant of variation and write equation of variation for every example given below.
(1)
; if
then ![](data:image/png;base64,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)
(2)
; when
then ![](data:image/png;base64,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)
(3)
; if
then ![](data:image/png;base64,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)
(4)
; if
then ![](data:image/png;base64,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)
Answer:(1)
(
,
)
![](data:image/png;base64,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)
(k=constant)
![](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,iVBORw0KGgoAAAANSUhEUgAAADoAAAAsCAMAAAAD6lucAAAAAXNSR0IArs4c6QAAAHhQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOjpmOjqQOmaQOma2OpC2OpDbZgAAZjoAZjo6ZrbbZrb/kDoAkGYAkGY6kLaQkLbbkNv/tmYAtmY6ttv/tv//25A627Zm27aQ29uQ29v/2////7Zm/9uQ/9u2//+2///bL1yxygAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABQUlEQVRIS91U0VbCMAxth6PoBJWpOHQO243+/x+apOtUHlgSHvSYB852yO29vVmuMX+84t6VHjTGJ2uvXyVig6s+sD/WpR/qxRsfG9xDag7FC/zYLRt63CzH3gYJv17nT5hoUC9C6dqsahbPd9ZWnq6aLszCYau99aZzaw2UWJrSZ8H56rPco8AWLBptWs9icgMBkNW0OBfJcHq39OYdUWiuwCUg7MHgqx2KGODphusv+1rsRpgY1kq0CuPp9Dl2TrIKWVescbpkubQSNFj+jCeGS1m7lB34wZBrWLjS54ssLmCdztV03rcH3Cf2EpwefgKVCVazShLqp2J0iZ0zc5b/p/8xKqpHxaKYnnJYs2MUiKIwnBw/bnAxe6cQ/DvQnCcKwaYtdma4Vzkc9zDWg8amZLXK4Yuhqtgl1gDBliz+BCryFiuBht4GAAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
∴constant of variation is 60 and equation is ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFQAAAAVCAMAAADvsTk6AAAAAXNSR0IArs4c6QAAAJBQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOjo6OjpmOjqQOmaQOma2OpC2OpDbZgAAZjoAZjo6ZjpmZmaQZrbbZrb/kDoAkGYAkGY6kLaQkLbbkNvbkNv/tmYAtmY6tpA6ttv/tv//25A625Bm27Zm27aQ29uQ29u229v/2////7Zm/9uQ/9u2//+2///bzwd2DAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABWElEQVQ4T+1T21KDMBDNUtvGCxa8oVaplbZWEsj//527mw1oMYzOOOOD5iGQ5OzZPXsSpf7H3+mAW+lZjXLdHcDp+md0G52+EpMrZnVTTJ4HrO2l32vk+4W0Rl97lEkecYIbmpKHJw2pRLtiSqxtFjaUzQHSW0RGRpvN5aSkIv3SwMlabWHRsWJ7eqCyeoG6KH1kcGlBPZFSe3mT2tGz7vN5WKmyw/B5CWGQVt6Z3JOWWjg8k8/EsSEj9Is2IwlWRytFFee12rEeCntPWvWmIexbpAzGojxd6OnHSvFsn3esh5UO5EvjqCgxiqRJT4OFDMJ00g1XeDPjRjEVt6/yt4mghsRuQtslcW9/lSxVczFCajUWsCUAGS/xBo41HC3FpebKl2jlq9wKrX2JG4VQNH/K8Q3+nXH8mLRwIUbc//z2/hqp6R5c5FkdbFsNIy54sMFXFLd/mOcNG/UiPyTvHgQAAAAASUVORK5CYII=)
(2)
(
,
)
![](data:image/png;base64,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)
(k=constant)
(1)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
(from 1)
∴constant of variation is 60 and equation is ![](data:image/png;base64,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)
(3)
(
,
)
![](data:image/png;base64,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)
(k=constant)
(1)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
(from 1)
∴constant of variation is 100 and the equation is ![](data:image/png;base64,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)
(4)
(
,
)
![](data:image/png;base64,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)
(k=constant)
(1)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADQAAAAyCAMAAAAk/wjEAAAAAXNSR0IArs4c6QAAAJBQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOjoAOjo6OjqQOmY6OmaQOma2OpCQOpDbZgAAZgBmZjoAZjo6ZjpmZmYAZpDbZrb/kDoAkDo6kDpmkGYAkGY6kNu2kNv/tmYAtmY6tmZmtrZmttv/tv//25A627Zm27aQ27a22////7Zm/9uQ/9u2//+2///bh1CbkwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABaklEQVRIS+1UWVPCMBDOFsUotlILQlQkeERtQ/L//5275Jhx6pDkhQfGPHWme33HLmPn8b4W21Ig+w4mH4VJun5XxUnY4z/JE31CIqpSR9gNB4CLVaEnzj9cAkx7BbB2UHUHl1vTzhPAJQpgRcjhK/Y5eUtqYgV2CpXltMcK11dJhjW/bXyQm0uFWRlDSf94FK3iNC5pwHapZ5YPYf9dkkyfA/uIbHkQVuCH6dI8SCw+gGcCJ7WvL+38+/i9ElBhJ/BZdoMysR00Y1SoZXgpwPE/osiOjYF6lqZ0VHVICz6eRHqjlcxo7kvvP7l/1ltBC6E5VLndyNJkbdQ0KX2suSPCDwdTZTPiIGm+ZgV6OcLJmjkr4OdTjnCcL5/6MJNp75YZ1O8X1CN6SIZ1OMa6qrsDzYGxIb2fVG6ggxGBZDqQFLVPBASBZfONy+wgWdE85wqLB8SdRfRenb1TqropX1rT5lH2W4WRRX8A3YsfNifXeOEAAAAASUVORK5CYII=)
![](data:image/png;base64,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)
(from 1)
∴constant of variation is 45 and equation is
![](data:image/png;base64,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)
Question 3.The boxes are to be filled with apples in a heap. If 24 apples are put in a box then 27 boxes are needed. If 36 apples are filled in a box how many boxes will be needed?
Answer:The number of apples and number of boxes will be inversely proportional as if the number of apples will be filled in a box then fewer boxes will be needed.
![](data:image/png;base64,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)
Number of apples in a box ![](data:image/png;base64,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)
Number of boxes needed ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACYAAAAVCAMAAAAdDWyfAAAAAXNSR0IArs4c6QAAAE5QTFRFAAAA///b//+22///tv///9u2/9uQkNv//7Zm27aQZrb/Zrbb25A6OpDbtmYAAGa2kDoAZjoAADqQADpmZgAAOgA6OgAAAABmAAA6AAAAz+33pAAAAAF0Uk5TAEDm2GYAAACFSURBVHja3ZDJEsIgEEQbowERhiy4zP//qMVampB4tfJuFD093QMcEnEdmWcJwHBk6loy4hsu/nkGSAPoH7rpRi4alU8TBrZQRXbydicgFQ/zkilJIb0TNZAY3E7ZwS6XN1XVgvI1WkvJdXX5dgETHJT9arKmv0tAkP1xjRwjCNRn+z/lDbp8B6fwjTsWAAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
(k=constant)
(1)
In the case, if 36 apples are filled in a box
Let the number of boxes be x
![](data:image/png;base64,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)
(k=constant)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEkAAAAoCAMAAACFBScRAAAAAXNSR0IArs4c6QAAAIRQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOjoAOjqQOmY6OmaQOma2OpC2OpDbZgAAZgA6ZjoAZjpmZmYAZmZmZpDbZrbbZrb/kDoAkDo6kGY6kLaQkLbbkNv/tmYAtmY6ttv/tv//25A627Zm27aQ29v/2////7Zm/9uQ/9u2//+2///bYN1i9gAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABq0lEQVRIS+2W21LCMBCGkyJEBalnKkLUiE3bvP/7uYeUFoGZbGGcccbcQNvs1z392yj191d4M+OSw3DZGn8+L7XOnsSReTP7ikaVIZLLnoGm50KUN2DGq8kfkRSKCV7Z1tFEYJOTGS07931S9yCJ5fWi3eevSiIprzE6Tln6sqPXO61nkPHmdq2YpDYGMi4EhULflGA5h+xAhoHkFqqCS+U6Z5P8CgXlFbLrdVwLvhefJFFwU9zvRh9kQtHFIth4L5XF+9uKx9q1fqZCaF9lJiV0YSwg97jD3Mk7s4LSXaz47ZArQqFa2nsiv35lcyD3Ymv1pC5/uc1Wqi64S3tSl4OURfFxk/akPgDEJtQpfakPJNXL6TvVdSv1YaAm13pKgtpKnf1sxSWR+sZAdJ3Uj3i0JR/8E408DOJO6sNiYyucMj+kLo6OhhYne1fqYscCNmVN82pX6mKSqpcwiHE2A6ondTno32IvA9D+49LpU9VFSoKCh+JEmZKD2MVOej45XNzKXM/OVPZ4Djud1tw/CD+7R94ZXtZnmLCYcItnFfGRcN8tmIkZ+KR3UN9GCCB7FRhKGgAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
Therefore, 18 boxes are needed.
Question 4.Write the following statements using the symbol of variation.
(1) The wavelength of sound (l) and its frequency (f) are in inverse variation.
(2) The intensity (I) of light varies inversely with the square of the distance (d) of a screen from the lamp.
Answer:(1) Wavelength of sound (l) and frequency (f) are in inverse proportion.
![](data:image/png;base64,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)
(2) Intensity (I) of light varies inversely
With the square of the distance (d)
![](data:image/png;base64,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)
Question 5.
and when x = 40 then y = 16. If x = 10, find y.
Answer:We are given that ![](data:image/png;base64,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)
When
then ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
(k=constant)
(1)
If ![](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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)
![](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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)
![](data:image/png;base64,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)
Question 6.X varies inversely as y, when x = 15 then y = 10, if x = 20 then y =?
Answer:We are given that x varies inversely as y
i.e. ![](data:image/png;base64,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)
When ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
(k=constant)
(1)
If ![](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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(from 1)
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The information about numbers of workers and the number of days to complete work is given in the following table. Complete the table.
Answer:
Number of workers and the number of days to complete a work will be inversely proportional because if the number of workers increases the number of days to complete the work will reduce.
When the number of workers
Number of days
[k = constant]
- (1)
The value of k will remain the same in all the cases
When the number of days
Number of workers
Number of workers (k=constant)
Number of workers(from 1)
Number of workers
∴ Number of workers15 when the number of days is 12
When the number of workers
Number of days (from 1)
Number of days
∴When the number of workers=10, number of days is 18
When the number of days
Number of workers
Number of workers
Number of workers (from1)
Number of workers
∴When the number of days is 36, the number of workers will be 5
Question 2.
Find constant of variation and write equation of variation for every example given below.
(1) ; if
then
(2) ; when
then
(3) ; if
then
(4) ; if
then
Answer:
(1) (
,
)
(k=constant)
∴constant of variation is 60 and equation is
(2) (
,
)
(k=constant)
(1)
(from 1)
∴constant of variation is 60 and equation is
(3) (
,
)
(k=constant)
(1)
(from 1)
∴constant of variation is 100 and the equation is
(4) (
,
)
(k=constant)
(1)
(from 1)
∴constant of variation is 45 and equation is
Question 3.
The boxes are to be filled with apples in a heap. If 24 apples are put in a box then 27 boxes are needed. If 36 apples are filled in a box how many boxes will be needed?
Answer:
The number of apples and number of boxes will be inversely proportional as if the number of apples will be filled in a box then fewer boxes will be needed.
Number of apples in a box
Number of boxes needed
(k=constant)
(1)
In the case, if 36 apples are filled in a box
Let the number of boxes be x
(k=constant)
Therefore, 18 boxes are needed.
Question 4.
Write the following statements using the symbol of variation.
(1) The wavelength of sound (l) and its frequency (f) are in inverse variation.
(2) The intensity (I) of light varies inversely with the square of the distance (d) of a screen from the lamp.
Answer:
(1) Wavelength of sound (l) and frequency (f) are in inverse proportion.
(2) Intensity (I) of light varies inversely
With the square of the distance (d)
Question 5.
and when x = 40 then y = 16. If x = 10, find y.
Answer:
We are given that
When then
(k=constant)
(1)
If
Question 6.
X varies inversely as y, when x = 15 then y = 10, if x = 20 then y =?
Answer:
We are given that x varies inversely as y
i.e.
When
(k=constant)
(1)
If
(from 1)
Practice Set 7.3
Question 1.Which of the following statements is of inverse variation?
(1) The number of workers on a job and time taken by them to complete the job.
(2) The number of pipes of the same size to fill a tank and the time taken by them to fill the tank.
(3) Petrol filled in the tank of a vehicle and its cost.
(4) Area of the circle and its radius.
Answer:(1) Yes, it is of inverse variation because more the number of workers will be lesser time will be taken.
(2) Yes, it is of inverse variation because more the number of pipes will be lesser time will be taken.
(3) No, it is not of inverse variation because the cost of petrol will increase with respect to its quantity.
(4) No, it is not of inverse variation because a larger circle has a longer radius.
Question 2.If 15 workers can build a wall in 48 hours, how many workers will be required to do the same work in 30 hours?
Answer:The number of workers building a wall and time taken by them is inversely proportional.
Let x be the number of workers and y be the time taken.
![](data:image/png;base64,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)
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(k is constant) (1)
Number of workers given=15
Time took =48 hrs
(Put in 1)
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![](data:image/png;base64,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)
Wall has to be built in 30 hours
So, ![](data:image/png;base64,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)
(Put in 1)
![](data:image/png;base64,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)
(Since
)
![](data:image/png;base64,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)
So, 24 workers are needed to build the wall in 30 hours.
Question 3.120 bags of half liter milk can be filled by a machine within 3 minutes find the time to fill such 1800 bags?
Answer:Number of bags will be directly proportional to the time taken because as the number of bags increases, time to fill them also increases.
Number of bags
0
Time is taken to fill![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
(k=constant)
![](data:image/png;base64,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)
(1)
Number of bags![](data:image/png;base64,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)
Let time taken to fill them be x
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
(From 1)
![](data:image/png;base64,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)
So, 45 minutes are needed to fill 1800 bags.
Question 4.A car with a speed of 60 km/hr takes 8 hours to travel some distance. What should be the increase in the speed if the same distance is to be covered in
hours?
Answer:Speed of car and time will be inversely proportional because as the speed increases, time for the journey decreases.
Speed of car![](data:image/png;base64,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)
Time ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
(k=constant)
(1)
Time for which distance is to be covered![](data:image/png;base64,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)
![](data:image/png;base64,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)
Let increase in speed![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABsAAAAVCAMAAACAAGUXAAAAAXNSR0IArs4c6QAAAEtQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOmY6Oma2OpDbZgAAZjpmZmYAZrb/kDoAkDo6kNv/tmYAtv//25A62////7Zm/9uQ//+2///bnU0dvQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAXUlEQVQoU+VRSRKAMAgjdd9qsWr5/0tFpzfp0ZM5EpIJgeh3YKDeI7BYl7MLJP6mdC1DRw/Eq24o9HW2XV+sMmaLtyelaa42WyhrSGNjcsKa44AVRjyc6mCSnz77AqzLAvxDciHSAAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
From 1
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACwAAAAVCAMAAAAKL/xWAAAAAXNSR0IArs4c6QAAAFpQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOgBmOjpmOjqQOma2OpC2OpDbZgAAZgA6ZmY6ZmZmZrb/kDoAkNv/tmYAttv/tv//25A627Zm2////7Zm/9uQ//+2///bnlD2DAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAqUlEQVQ4T92RyQ7CMAxE7ZaWraU0DTHN8v+/ibM0Qir4isQccplna8YB+HcRIs5gEQ+rVJWaJdpPHPjVnci6PsNBtQbc0Uh7/XjPMLi+C2oWz60HW2CgZrqIrD2vFfYjB9mkuXDWtgv8bYEKB5U6flNQ7DJMKSpd9dvq3QyfNSvC7mS4oxAjWiVGugSlMUEFpvh13PEhwvkHFcZ2fINa/tMQ5xZ9OdYv3RcVNgfjJOT57wAAAABJRU5ErkJggg==)
So, speed should be increased by 4 km/hr.
Which of the following statements is of inverse variation?
(1) The number of workers on a job and time taken by them to complete the job.
(2) The number of pipes of the same size to fill a tank and the time taken by them to fill the tank.
(3) Petrol filled in the tank of a vehicle and its cost.
(4) Area of the circle and its radius.
Answer:
(1) Yes, it is of inverse variation because more the number of workers will be lesser time will be taken.
(2) Yes, it is of inverse variation because more the number of pipes will be lesser time will be taken.
(3) No, it is not of inverse variation because the cost of petrol will increase with respect to its quantity.
(4) No, it is not of inverse variation because a larger circle has a longer radius.
Question 2.
If 15 workers can build a wall in 48 hours, how many workers will be required to do the same work in 30 hours?
Answer:
The number of workers building a wall and time taken by them is inversely proportional.
Let x be the number of workers and y be the time taken.
(k is constant) (1)
Number of workers given=15
Time took =48 hrs
(Put in 1)
Wall has to be built in 30 hours
So,
(Put in 1)
(Since
)
So, 24 workers are needed to build the wall in 30 hours.
Question 3.
120 bags of half liter milk can be filled by a machine within 3 minutes find the time to fill such 1800 bags?
Answer:
Number of bags will be directly proportional to the time taken because as the number of bags increases, time to fill them also increases.
Number of bags0
Time is taken to fill
(k=constant)
(1)
Number of bags
Let time taken to fill them be x
(From 1)
So, 45 minutes are needed to fill 1800 bags.
Question 4.
A car with a speed of 60 km/hr takes 8 hours to travel some distance. What should be the increase in the speed if the same distance is to be covered in hours?
Answer:
Speed of car and time will be inversely proportional because as the speed increases, time for the journey decreases.
Speed of car
Time
(k=constant)
(1)
Time for which distance is to be covered
Let increase in speed
From 1
So, speed should be increased by 4 km/hr.