Question

The ratio of the ages of A and B seven years ago was 3 : 4 respectively. The ratio of their ages nine years from now will be 7 : 8 respectively. What is B's age at present?

Options

• 16 years

• 19 years

• 28 years

• 23 years

Answer 1

23 years

Explanation:

A's present age = (3x + 7) years

B's present age = (4x + 7) years

After 9 years,

`(3"x" + 7 + 9)/(4"x" + 7 + 9) = 7/8`

⇒ `(3"x" + 16)/(4"x" + 16) = 7/8`

⇒ `(3"x" + 16)/("x" + 4) = 7/2`

⇒ 7x + 28 = 6x + 32

⇒ x = 32 − 28 = 4

∴ B's present age = 4x + 7 = 4 × 4 + 7 = 23 years