Question

The ratio of the present ages of mother and son is 12 : 5. The mother's age, at the time of birth of the son was 21 years. Find their present ages.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{common}\mathrm{multiple}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{ratios}\mathrm{be}x. \\ \mathrm{Thus},\mathrm{we}\mathrm{have}: \\ \mathrm{Present}\mathrm{age}\mathrm{of}\mathrm{the}\mathrm{mother}=12x\mathrm{yrs} \\ \mathrm{Present}\mathrm{age}\mathrm{of}\mathrm{the}\mathrm{son}=5x\mathrm{yrs} \\ \mathrm{Now}, \\ \mathrm{Let}\mathrm{the}\mathrm{son}\mathrm{be}\mathrm{born}n\mathrm{years}\mathrm{ago}. \\ \mathrm{Age}\mathrm{of}\mathrm{the}\mathrm{son}\mathrm{before}n\mathrm{years}=\left(5x-n\right)\mathrm{yrs} \\ \mathrm{Age}\mathrm{of}\mathrm{the}\mathrm{mother}\mathrm{before}n\mathrm{years}=\left(12x-n\right)\mathrm{yrs} \\ \mathrm{We}\mathrm{know}: \\ \mathrm{Age}\mathrm{of}\mathrm{the}\mathrm{son}\mathrm{at}\mathrm{the}\mathrm{time}\mathrm{of}\mathrm{his}\mathrm{birth}=0\mathrm{yrs} \\ \mathrm{Thus},\mathrm{we}\mathrm{have}: \\ 5x-n=0 \\ 5x=n...\left(\mathrm{i}\right) \\ \mathrm{According}\mathrm{to}\mathrm{the}\mathrm{question}, \\ 12x-n=21 \\ \Rightarrow 12x-5x=21[\mathrm{From}(\mathrm{i}\left)\right] \\ \Rightarrow 7x=21 \\ \Rightarrow x=3 \\ \therefore \mathrm{Present}\mathrm{age}\mathrm{of}\mathrm{the}\mathrm{mother}=12\times 3=36\mathrm{yrs} \\ \mathrm{And}, \\ \mathrm{Present}\mathrm{age}\mathrm{of}\mathrm{the}\mathrm{son}=5\times 3=15\mathrm{yrs} \end{gathered}$$