Question

the age of a father 8 years back was 5 times that of his son after 8 years his age will be 8 years more than double the age of his son find their present ages

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{son}=\mathrm{x}\mathrm{yrs} \\ \mathrm{Let}\mathrm{the}\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{father}=\mathrm{y}\mathrm{yrs} \\ \mathbf{5}\mathbf{}\mathbf{YEARS}\mathbf{}\mathbf{AGO}\mathbf{}\mathbf{:} \\ \mathrm{son}\text{'}\mathrm{s}\mathrm{age}=\left(\mathrm{x}-5\right)\mathrm{yrs} \\ \mathrm{father}\text{'}\mathrm{s}\mathrm{age}=\left(\mathrm{y}-5\right)\mathrm{yrs} \\ \mathrm{Now},\mathrm{according}\mathrm{to}\mathrm{question}: \\ \mathrm{y}-5=5\left(\mathrm{x}-5\right) \\ \Rightarrow \mathrm{y}-5=5\mathrm{x}-25 \\ \Rightarrow \mathrm{y}=5\mathrm{x}-20.....\left(1\right) \\ \mathbf{AFTER}\mathbf{}\mathbf{8}\mathbf{}\mathbf{YEARS}\mathbf{}\mathbf{:} \\ \mathrm{son}\text{'}\mathrm{s}\mathrm{age}=\left(\mathrm{x}+8\right)\mathrm{yrs} \\ \mathrm{father}\text{'}\mathrm{s}\mathrm{age}=\left(\mathrm{y}+8\right)\mathrm{yrs} \\ \mathrm{Now},\mathrm{according}\mathrm{to}\mathrm{question}: \\ \mathrm{y}+8=2\left(\mathrm{x}+8\right)+8 \\ \Rightarrow \mathrm{y}+8=2\mathrm{x}+24 \\ \Rightarrow \mathrm{y}=2\mathrm{x}+16......\left(2\right) \\ \mathrm{From}\left(1\right)\mathrm{and}\left(2\right),\mathrm{we}\mathrm{get} \\ 5\mathrm{x}-20=2\mathrm{x}+16 \\ \Rightarrow 3\mathrm{x}=36 \\ \Rightarrow \mathrm{x}=12 \\ \mathrm{now},\mathrm{from}\left(1\right),\mathrm{we}\mathrm{get} \\ \mathrm{y}=5\times 12-20=40 \\ \mathrm{So},\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{son}=12\mathrm{yrs} \\ \mathrm{present}\mathrm{age}\mathrm{of}\mathrm{father}=40\mathrm{yrs} \end{gathered}$$