Question

Q.19. The difference between the ages of two sisters is 10 years. If 15 years ago, the elder one was twice as old as the younger one, find their present ages.

Answer 1

Dear student
$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{age}\mathrm{of}\mathrm{younger}\mathrm{sister}\mathrm{be}\mathrm{x}. \\ \mathrm{Then}\mathrm{age}\mathrm{of}\mathrm{elder}\mathrm{sister}\mathrm{will}\mathrm{be}\left(\mathrm{x}+10\right) \\ 15\mathrm{years}\mathrm{ago}: \\ \mathrm{Age}\mathrm{of}\mathrm{younger}\mathrm{sister}=\mathrm{x}-15 \\ \mathrm{Age}\mathrm{of}\mathrm{elder}\mathrm{sister}=\left(\mathrm{x}+10-15\right) \\ =\mathrm{x}-5 \\ \mathrm{So},\left(\mathrm{x}-5\right)=2\left(\mathrm{x}-15\right) \\ \Rightarrow \mathrm{x}-5=2\mathrm{x}-30 \\ \Rightarrow 25=\mathrm{x} \\ \mathrm{So},\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{younger}\mathrm{sister}\mathrm{is}25\mathrm{yrs}. \\ \mathrm{Present}\mathrm{age}\mathrm{of}\mathrm{elder}\mathrm{sister}=\left(\mathrm{x}+10\right)=25+10=35\mathrm{yrs}. \end{gathered}$$
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