Question

The ages of A and B are in the ratio 4 : 3. After 6 years, their ages will be in the ratio 11 : 9. A's present age is

(a) 12 years
(b) 16 years
(c) 20 years
(d) 24 years

Answer 1

$$\begin{gathered} \left(\mathrm{b}\right)12\mathrm{years} \\ \mathrm{Let}\mathrm{the}\mathrm{ages}\mathrm{of}\mathrm{A}\mathrm{and}\mathrm{B}\mathrm{be}x\mathrm{and}y\mathrm{years},\mathrm{respectively}. \\ \begin{array}{l}\text{Now,}\frac{x}{y}=\frac{4}{3}\\ \Rightarrow 3x=4y\\ \Rightarrow x=\frac{4}{3}y\\ \text{After 6 years, we have:}\\ \frac{\text{x + 6}}{y+6}=\frac{11}{9}\\ \Rightarrow \frac{\frac{4}{3}y+6}{y+6}=\frac{11}{9}\\ \Rightarrow \frac{4y+18}{\text{3(y}+6)}=\frac{11}{9}\\ \Rightarrow 36y+162=33y+198\\ \Rightarrow 3y=36\\ \Rightarrow y=12\\ \therefore x=\frac{4}{\sout{3}}\times \sout{1}{\sout{2}}^4=16\\ \text{Hence, A's present age is 16 years.}\end{array} \\ \begin{array}{}\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \end{array} \end{gathered}$$