Question

Rahim's age and his wife's age are in the ratio 4 : 3. After 4 years, the ratio of their ages will be 9 : 7. Find Rahim's age.

• A. 30 years
• B. 32 years
• C. 24 years
• D. 38 years

Answer 1

The correct option is B

32 years

Let Rahim's present age be $4x$ years.

$\Rightarrow$ Present age of Rahim’s wife will be $3x$ years.

After 4 years, Rahim's age will be $(4x+4)$ years and his wife’s age will be $(3x+4)$ years.

After 4 years, the ratio of their ages will be 9 : 7 (given).

$\therefore \frac{4x+4}{3x+4}=\frac{9}{7}$

$\Rightarrow 28x+28=27x+36$

$\Rightarrow x=8$

$\therefore$ Rahim's age = $4x$ = $4\times 8=32$ years