Question

The ages of A and B are in the ratio 8 : 3. Six years hence, their ages will be in the ratio 9 : 4. Find their present ages.

Answer 1

Suppose that the present ages of A and B are 8x yrs and 3x yrs.
Then, (8x + 6) : (3x + 6) = 9 : 4
⇒ $\frac{8x+6}{3x+6}=\frac{9}{4}$
⇒ 32x + 24 = 27x + 54
⇒ 5x = 30
⇒ x = 6

Now, present age of A = 8 $\times$ 6 yrs = 48 yrs
Present age of B = 3 $\times$ 6 yrs = 18 yrs