1. Suresh scored
15 marks more than Ramesh in Mathematics. If the sum of their marks in
Mathematics is 275, find the marks obtained by each of them.

**Ans. Suresh :- 145; Ramesh :- 130 marks**
2. The sum of two
numbers is 40 and the greater number is thrice the smaller number. Find the
numbers.

**Ans. The greater number is 30 & the smaller number is 10.**
3. The sum of the
two numbers is 25 and the difference between them is 15. Find the two numbers.

**Ans. The greater number is 20 and the smaller number is 5.**
4. The length of
a rectangle is greater than twice its breadth by 4 cm. If the perimeter of the
rectangle is 26 cm, find its length and breadth.

**Ans. Length of the rectangle is 10cm & its breadth is 3 cm.**
5. The sum of the
present ages of Ram and Shyam is 36 years. Ram is elder than Shyam by 2 years.
Find their present ages.

**Ans. The present age of Ram is 19 yrs. And Shyam is 17 years.**
6. Ram has in all
35 coins, some of denomination 25 paise and some of 10 paise. Total amount is
Rs. 6.20. Find the number of coins of each kind.

**Ans. 25 paise coins; - 18 and 10 paise coins: - 17.**
7. Cost of a
table is three times the cost of a chair. One table and one chair together cost
Rs. 800. Find the cost of a table. Ans.

**600**
8. The perimeter
of an isosceles triangle is 43cm. The length of its each congruent side is 1 cm
less than twice the length of its base. Find the length of each side of the
triangle.

**Ans. 17 cm, 9 cm, 17 cm.**
9. The difference
between two numbers is 5. Six times the smaller number is equal to four times
the greater. Find the numbers.

**Ans. 15 and 10.**
10.
In
a right – angled triangle, one of the acute angles exceeds the other by 20

^{0}. Find the measure of the acute angles.**Ans. 35**^{0 }& 55^{0}.
1. The perimeter
of an isosceles triangle is 27 cm and the length of the congruent sides is
greater than twice the length of the base by 1 cm. Find the length of each side
of the triangle.

**Ans. 11 cm, 11cm and 5 cm.**
2. Ina a cyclic
quadrilateral ABCD, measure of angle A is double the measure of angle C. Find
the measure of angle A and angle C.

**Ans. 120**^{0 }& 60^{0}.
3. The sum of two
numbers is 70. Three times the greater number is equal to four times the
smaller number. Find the two numbers.

**Ans. 40 and 30.**
4. The difference
between two numbers is 16. The greater number is 1 more than twice the smaller
number. Find the numbers.

**Ans. 31 and 15.**
5. 2 pens and 3 pencils
cost Rs. 26, while 3 pens and 2 pencils cost Rs. 34. Find the cost of a pen and
a pencil.

**Ans. Pen: - Rs. 10 Pencil: - Rs. 2.**
6. In a
parallelogram ABCD, the measure of angle A is thrice the measure of angle B.
Find the measure of angle A and angle B.

**Ans. Angle A :- 135**^{0}& angle B :- 45^{0}.
7. A piece of
string 12m in length was cut into two pieces such that one piece is x metres
and the other is y meters. If y is 2 meters more than x, find the length of
each piece.

**Ans. 5m and 7 m.**
8. The difference
between the measures of angle A and angle B of a parallelogram ABCD is 18

^{0}. Find the measure of angle A and angle B.**Ans. Angle A: - 99**and^{0 }**Angle B: - 81**^{0}.
9. 2 mangles and
5 oranges together cost Rs. 30; but 4 mangoes and 3 oranges cost Rs. 46. Find
the cost of a mango and an orange.

**Ans. Mango 10Rs, Orange 2 Rs.**
10.
3
books and 1 notebook together cost Rs. 53, but 2 books and 4 notebooks cost Rs.
62. Find the cost of a book and a note book.

**Ans. Book Rs. 15, Note book Rs. 8.**
1. 3 pepsi and 1
mangola bottles together cost Rs. 53, but 2 pepsi and 4 mangola bottles cost
Rs. 62. Find the cost of a pepsi and a mangola bottle.

**Ans. Cost of pepsi bottle: - Rs. 15 Mangola bottle: - Rs. 8.**
2. Out of 10
litres, a milkman sells some milk at the rate of Rs. 15 per litre and some at
the rate of Rs.12 per litre. He gets Rs. 141 on selling it. Find the quantity
of milk he sold at each rate.

**Ans. 7 litres @ Rs. 15 per litre and 3 litres @ Rs. 12 per litres.**
3. Mother’s age
is 4 times her daughter’s age. 16 years hence mother’s age will be twice her
daughter’s age at that time. Find their present ages.

**Ans. Mother’s present age ; 32 years. daughter’s present age : 8 years.**
4. The sum of the
present ages of Mangesh and his mother is 70 years. Seven years ago mother’s
age was three times the age of Mangesh at that time. Find their present ages.

**Ans. Mangesh: - 21 years. Mother: - 49 years.**
5. Some postcards
costing 25 paise each and inland letters costing Rs. 2 each were purchased for
Rs. 53. Total number of postcards and inland letters purchased was 44. If the
number of postcards and inland letters is interchanged, how much less would be
the amount?

**Rs. 7 less.**
6. If 3 is added
to the numerator and 5 is subtracted from the denominator of a fraction, the
value of the fraction becomes ¾ and if 1 is added to the numerator and 3 is
subtracted from the denominator, the value of the fraction becomes ½. Find the
original fraction.

**Ans. The original fraction is 6/17.**
7. Sum of two
numbers is 200. 1/3 of greater number is equal to ½ of smaller number. Find the
numbers.

**Ans. 120 & 80.**
8. On the first
day of the sale of tickets of a drama, 50 tickets in all were sold. If the
rates of the tickets were Rs. 20 and Rs. 40 per ticket and the total collection
was Rs. 1,800, find the number of tickets sold at each rate.

**Ans. 10 tickets @ Rs. 20, 40 tickets @ Rs. 40.**
9. Age of John’s
father is three times the age of John. Five years ago, age of father was four
times John’s age at that time. Find their present ages.

**Ans. Father’s age :- 45 yrs. John’s age :- 15 yrs. B**
10.
The length of a rectangle is less than twice
its breadth by 9cm. The perimeter of the rectangle is 54 cm. Find the area of
the rectangle.

**Ans. Area is 180 sq cm.**
1. If I divide
the sum of two numbers by 3, the quotient is 4 and the remainder 1. If I divide
the difference of these two numbers by 2, the quotient is 2 and the remainder
1. Find the number.

**Ans. 9 and 4.**
2. Ramesh
distributed certain number of pencil among his friends. If the number of
friends were 4 more, then each would have got 1 pencil less. But if the number
of friends were 4 less, then each would have received 2 pencils more. Find the
number of friends and total number of pencils distributed.

**Ans. Friends :- 12 pencils : 48**
3. 3 pens and 4
pencils cost Rs. 38, while 2 pens and 5 pencils cost Rs. 30. Find the cost of
each pen and each pencil.

**Ans. Pen Rs. 10 and Pencil Rs. 2.**
4. If the
numerator of a fraction is decreased by 1, its value becomes ½ and if its
denominator is increased by 7, its value becomes 1/3. Find that fraction.

**Ans. The fraction is 5/8.**
5. If one is
subtracted from the numerator and denominator, the value of the fraction
becomes 1/3. When 3 is added to its numerator and denominator, the value
becomes ½. Find the fraction.

**Ans. The fraction is 5/13.**
6. The value of the fraction becomes 2/5, if 2 is
subtracted from its numerator and the value becomes ½, if 1 is added to its
denominator. Find the fraction.

**Ans. 8/15.**
7. Some amount is
distributed equally among some boys. If 10 boys were more each would get Rs. 2
less and each would get Rs. 6 more if 15 boys were less. Find the amount
distributed and the number of boys.

**Ans. 40 boys and Rs. 400.**
8. Students were
standing in rows for P.T exercises. If 4 students were less in each row, 10
more rows were required and if 5 students were more in each row, then the
number of rows were reduced by 8. Find the number of students.

**Ans.****800 students.**
9. If 1 is added
to the numerator of a certain fraction, it becomes ½. Instead, if 5 are
subtracted from its denominator, it becomes 1. Find the fractions.

**Ans. 3/8**
10.
A
certain amount is distributed equally among certain boys. If there were 5 boys
more each would have received Rs. 8 less, while if there were 4 boys less, each
would have received Rs. 10 more. Find the amount distributed and the number of
boys.

**Ans. Rs. 800 boys 20.**
11.
The
perimeter of a rectangle is 40 cm and its length is 5 cm more than twice its
breadth. Find the length and the breadth of the rectangle.

**Ans. Length = 15cm and breadth = 5 cm.**
12.
A
two – digit number is 4 times the sum of its digits. The number obtained by
interchanging the digits is greater by 9 than the original number. Find the
original number.

**Ans. The original number is 12.**
13.
A
boat requires 6 hrs to travel 36 km downstream and 24 km upstream. It requires
9 hrs to travel 48 km downstream and 40 km upstream. Find the speed of the
stream and that of the boat in the still water.

**Ans. Speed of the Boat = 10Km/ hr. and the speed of the stream = 2 Km/ hr.**
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