Question

Mark (✓) against the correct answer
The ages of A and B are in the ratio 3 : 8. Six years hence, their ages will be in the ratio 4 : 9. The present age of A is

(a) 18 years
(b) 15 years
(c) 12 years
(d) 21 years

Answer 1

(a) 18 years

Suppose that the present ages of A and B are 3x yrs and 8x yrs, respectively.
After six years, the age of A will be (3x+6) yrs and that of B will be (8x+6) yrs.
Then, (3x +6) : (8x + 6) = 4 : 9

$$\begin{gathered} \Rightarrow \frac{3x+6}{8x+6}=\frac{4}{9} \\ \Rightarrow 27x+54=32x+24 \\ \Rightarrow 5x=30 \\ \Rightarrow x=6 \\ \mathrm{Hence},\mathrm{the}\mathrm{present}\mathrm{ages}\mathrm{of}\mathrm{A}\mathrm{and}\mathrm{B}\mathrm{are}18\mathrm{yrs}\mathrm{and}48\mathrm{yrs},\mathrm{respectively}. \end{gathered}$$