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?

विकल्प

• 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,

${\displaystyle \frac{3\text{x}+7+9}{4\text{x}+7+9}=\frac{7}{8}}$

⇒ ${\displaystyle \frac{3\text{x}+16}{4\text{x}+16}=\frac{7}{8}}$

⇒ ${\displaystyle \frac{3\text{x}+16}{\text{x}+4}=\frac{7}{2}}$

⇒ 7x + 28 = 6x + 32

⇒ x = 32 − 28 = 4

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