Question

THE AGES OF SHOBITH AND SHYAM ARE IN RATIO 7:5. IF SHOBITH WAS 9 YEARS YOUNGER AND SHYAM WAS 9 YEARS OLDER THEN AGE OF SHOBITH WOULD HAVE BEEN HALF THE AGE OF SHYAM. FIND HEIR PRESENT AGES.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{Shobith}\mathrm{be}7x\mathrm{years}\mathrm{and}\mathrm{that}\mathrm{of}\mathrm{Shyam}\mathrm{be}5x\mathrm{years}. \\ \mathrm{Now}\mathrm{age}\mathrm{of}\mathrm{Shobith}9\mathrm{years}\mathrm{ago}=\left(7\mathrm{x}-9\right)\mathrm{years}. \\ \mathrm{Age}\mathrm{ogf}\mathrm{Shyam}\mathrm{after}9\mathrm{years}=\left(5\mathrm{x}+9\right)\mathrm{years}. \\ \mathrm{It}\mathrm{is}\mathrm{given}\mathrm{in}\mathrm{the}\mathrm{question}\mathrm{that}\mathrm{age}\mathrm{of}\mathrm{Shobith}9\mathrm{years}\mathrm{ago}\mathrm{would}\mathrm{have}\mathrm{been} \\ \mathrm{half}\mathrm{of}\mathrm{the}\mathrm{age}\mathrm{what}\mathrm{Shyam}\mathrm{will}\mathrm{have}\mathrm{after}9\mathrm{years}. \\ \mathrm{Therefore}, \\ \left(7\mathrm{x}-9\right)=\frac{\left(5\mathrm{x}+9\right)}{2} \\ \Rightarrow 2\left(7\mathrm{x}-9\right)=\left(5\mathrm{x}+9\right) \\ \Rightarrow 14\mathrm{x}-18=5\mathrm{x}+9 \\ \Rightarrow 14\mathrm{x}-5\mathrm{x}=9+18 \\ \Rightarrow 9\mathrm{x}=27 \\ \Rightarrow \mathrm{x}=3 \\ \mathrm{Hence},\mathrm{the}\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{Shobith}=7\mathrm{x}=7\times 3=21\mathrm{years} \\ \mathrm{and}\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{Shyam}=5\mathrm{x}=5\times 3=15\mathrm{years}. \end{gathered}$$