Question

Rakhi's mother is four times as old as Rakhi. After 5 years, her mother will be three times as old as she will be then. Find their present ages.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{Rakhi}\mathrm{be}\mathrm{x}. \\ \mathrm{Then},\mathrm{the}\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{Rakhi}\text{'}s\mathrm{mother}\mathrm{will}\mathrm{be}4\mathrm{x}. \\ \mathrm{After}\mathrm{five}\mathrm{years},\mathrm{Rakhi}\text{'}\mathrm{s}\mathrm{age}\mathrm{will}\mathrm{be}(\mathrm{x}+5). \\ \mathrm{After}\mathrm{five}\mathrm{years},\mathrm{her}\mathrm{mother}\text{'}\mathrm{s}\mathrm{age}\mathrm{will}\mathrm{be}(4\mathrm{x}+5). \\ 4x+5=3(x+5) \\ \Rightarrow 4x+5=3x+15 \\ \Rightarrow 4x-3x=15-5 \\ \Rightarrow x=10 \\ \mathrm{Present}\mathrm{age}\mathrm{of}\mathrm{Rakhi}=10\mathrm{years} \\ \mathrm{Present}\mathrm{age}\mathrm{of}\mathrm{Rakhi}\text{'}\mathrm{s}\mathrm{mother}=4\left(\mathrm{x}\right)=4\times 10=40\mathrm{years} \end{gathered}$$