Class 7 Maths Algebric Expressions QA

Class 7 Algebric Expressions

Question 1: The sum of the ages of a father and his son is 48 years. After 12 years, the father's age will be twice the age of his son. Find their present ages.

Solution:

x + y = 48 ...(1)

x + 12 = 2(y + 12)

x + 12 = 2y + 24

x = 2y + 12 ...(2)

Put equation (2) in equation (1).

2y + 12 + y = 48

3y + 12 = 48

3y = 36

y = 12 years

x = 48 - 12

x = 36 years

Answer: Father = 36 years, Son = 12 years.

Question 2: The sum of the ages of a mother and her daughter is 42 years. After 5 years, the mother's age will be three times the age of her daughter. Find their present ages.

Solution:

x + y = 42 ...(1)

x + 5 = 3(y + 5)

x + 5 = 3y + 15

x = 3y + 10 ...(2)

Put equation (2) in equation (1).

3y + 10 + y = 42

4y + 10 = 42

4y = 32

y = 8 years

x = 42 - 8

x = 34 years

Answer: Mother = 34 years, Daughter = 8 years.

Question 3

The sum of the ages of two brothers is 24 years. The elder brother is twice as old as the younger brother. Find their present ages.

Solution:

Let elder brother's age = x years

Let younger brother's age = y years

x + y = 24 ...(1)

x = 2y ...(2)

Put equation (2) in equation (1).

2y + y = 24

3y = 24

y = 8 years

x = 2 × 8

x = 16 years

Answer: Elder brother = 16 years, Younger brother = 8 years.

Question 4

The sum of the ages of a father and his son is 60 years. The father is 4 times as old as his son. Find their present ages.

Solution:

Let father's age = x years

Let son's age = y years

x + y = 60 ...(1)

x = 4y ...(2)

Put equation (2) in equation (1).

4y + y = 60

5y = 60

y = 12 years

x = 4 × 12

x = 48 years

Answer: Father = 48 years, Son = 12 years.

Question 5: The sum of the ages of a mother and her son is 47 years. After 5 years, the mother's age will be twice the age of her son. Find their present ages.

Solution:

x + y = 47 ...(1)

x + 5 = 2(y + 5)

x = 2y + 5 ...(2)

Put equation (2) in equation (1).

2y + 5 + y = 47

3y = 42

y = 14 years

x = 47 - 14

x = 33 years

Answer: Mother = 33 years, Son = 14 years.

Question 6

The sum of the ages of a father and his son is 70 years. After 10 years, the father's age will be twice the age of his son. Find their present ages.

Solution:

Let father's age = x years

Let son's age = y years

x + y = 70 ...(1)

x + 10 = 2(y + 10)

x = 2y + 10 ...(2)

Put equation (2) in equation (1).

2y + 10 + y = 70

3y = 60

y = 20 years

x = 70 - 20

x = 50 years

Answer: Father = 50 years, Son = 20 years.

Question 7: The sum of the ages of a mother and her daughter is 53 years. Four years ago, the mother was four times as old as her daughter. Find their present ages.

Solution:

x + y = 53 ...(1)

x - 4 = 4(y - 4)

x = 4y - 12 ...(2)

Put equation (2) in equation (1).

4y - 12 + y = 53

5y = 65

y = 13 years

x = 53 - 13

x = 40 years

Answer: Mother = 40 years, Daughter = 13 years.

Question 8

The sum of the ages of two brothers is 36 years. After 6 years, the elder brother will be twice as old as the younger brother. Find their present ages.

Solution:

Let elder brother's age = x years

Let younger brother's age = y years

x + y = 36 ...(1)

x + 6 = 2(y + 6)

x = 2y + 6 ...(2)

Put equation (2) in equation (1).

2y + 6 + y = 36

3y = 30

y = 10 years

x = 36 - 10

x = 26 years

Answer: Elder brother = 26 years, Younger brother = 10 years.

Question 9

A father is 24 years older than his son. After 4 years, the father's age will be twice the age of his son. Find their present ages.

Solution:

Let father's age = x years

Let son's age = y years

x = y + 24 ...(1)

x + 4 = 2(y + 4)

x + 4 = 2y + 8

x = 2y + 4 ...(2)

Put equation (1) in equation (2).

y + 24 = 2y + 4

24 - 4 = 2y - y

y = 20 years

x = 20 + 24

x = 44 years

Answer: Father = 44 years, Son = 20 years.

Question 10

The sum of the ages of a father and his son is 64 years. Eight years ago, the father was five times as old as his son. Find their present ages.

Solution:

Let father's age = x years

Let son's age = y years

x + y = 64 ...(1)

x - 8 = 5(y - 8)

x - 8 = 5y - 40

x = 5y - 32 ...(2)

Put equation (2) in equation (1).

5y - 32 + y = 64

6y = 96

y = 16 years

x = 64 - 16

x = 48 years

Answer: Father = 48 years, Son = 16 years.