Question

Mark (✓) against the correct answer
The ages of A and B are in the ratio 5 : 2. After 5 years, their ages will be in the ratio 15 : 7. The present age of A is

(a) 48 years
(b) 36 years
(c) 40 years
(d) 35 years

Answer 1

(c) 40 years

Suppose that the present ages of A and B are 5x yrs and 2x yrs, respectively.
After 5 years, the ages of A and B will be (5x+5) yrs and (2x+5) yrs, respectively.

Then, (5x + 5) : (2x + 5) = 15 : 7

⇒ $\frac{5x+5}{2x+5}=\frac{15}{7}$

Cross multiplying, we get:

35x + 35 = 30x + 75
⇒ 5x = 40
⇒ x = 8

Hence, the present age of A is 5 $\times$ 8 = 40 yrs.