Question

Mother’s age is 7 times her son’s age. After 2 years, she will be 5 times his age.

∴ Their present ages are ______.

Options

• (3, 21)

• (5, 35)

• (4, 28)

• (6, 42)

Answer 1

Mother’s age is 7 times her son’s age. After 2 years, she will be 5 times his age.

∴ Their present ages are (4, 28).

Explanation:

Let the son’s present age be x,

Then the mother’s present age is 7x,

After 2 years:

Son’s age = x + 2,

Mother’s age = 7x + 2,

Given:

7x + 2 = 5(x + 2)

7x + 2 = 5x + 10

7x − 5x = 10 − 2

2x = 8

x = `8/2`

∴ x = 4

So: x = Son’s age = 4

Mother’s age = 7x

= 7(4)

= 28

Therefore, their present ages are 4 and 28.