Question

five years ago pooja was twice sanchi's age. five years hence, their age will be in the ratio 4:3. find their present ages?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{age}\mathrm{of}\mathrm{Sanchi}5\mathrm{years}\mathrm{ago}=x\mathrm{yrs} \\ \mathrm{Then}\mathrm{the}\mathrm{age}\mathrm{of}\mathrm{Pooja}5\mathrm{years}\mathrm{ago}=2x\mathrm{yrs} \\ \mathrm{Now}\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{Sanchi}=\left(x+5\right)\mathrm{yrs} \\ \mathrm{present}\mathrm{age}\mathrm{of}\mathrm{Pooja}=\left(2x+5\right)\mathrm{yrs} \\ \underline{\mathbf{After}\mathbf{}\mathbf{5}\mathbf{}\mathbf{years}}: \\ \mathrm{Sanchi}\text{'}\mathrm{s}\mathrm{age}=\left(x+10\right)\mathrm{yrs} \\ \mathrm{Pooja}\text{'}\mathrm{s}\mathrm{age}=\left(2x+10\right)\mathrm{yrs} \\ \mathrm{Now}\mathrm{according}\mathrm{to}\mathrm{question}, \\ \frac{2x+10}{x+10}=\frac{4}{3} \\ \Rightarrow 3\left(2x+10\right)=4\left(x+10\right) \\ \Rightarrow 6x+30=4x+40 \\ \Rightarrow 6x-4x=40-30 \\ \Rightarrow 2x=10 \\ \Rightarrow x=5 \\ \mathrm{So},\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{Sanchi}=5+5=10\mathrm{yrs} \\ \mathrm{present}\mathrm{age}\mathrm{of}\mathrm{Pooja}=2\times 5+5=10+5=15\mathrm{yrs} \end{gathered}$$