Question

The ages of A and B are in the ratio 5 : 3. After 6 years, their ages will be in the ratio 7 : 5. The present age of A is

(a) 5 years
(b) 10 years
(c) 15 years
(d) 20 years

Answer 1

$\begin{array}{l}\left(\text{c}\right)15\mathrm{years}\\ \text{Let the present ages of A and B be 5}x\text{and 3}x,\mathrm{respectively}.\\ \mathrm{According}\mathrm{to}\mathrm{the}\mathrm{question},\mathrm{we}\mathrm{have}:\\ \frac{5x+6}{3x+6}=\frac{7}{5}\\ \Rightarrow 25x+30=21x+42\\ \Rightarrow 25x-21x=42-30\\ \Rightarrow 4x=12\\ \Rightarrow x=\frac{\sout{1}{\sout{2}}^3}{\sout{4}}\\ \Rightarrow x=3\\ \therefore \text{A}’\text{s present age=5}\times \text{3 years=15 years}\end{array}$