Question

5 years hence the age of a father shall be 3 times the age of his son while 5 years earlier the age of the father was 7 times the age of his son . find their present age .

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{son}=\mathrm{x}\mathrm{yrs} \\ \mathrm{Let}\mathrm{the}\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{father}=\mathrm{y}\mathrm{yrs} \\ \mathbf{AFTER}\mathbf{}\mathbf{5}\mathbf{}\mathbf{YEARS}\mathbf{}: \\ \mathrm{son}\text{'}\mathrm{s}\mathrm{age}=\left(\mathrm{x}+5\right)\mathrm{yrs} \\ \mathrm{Father}\text{'}\mathrm{s}\mathrm{age}=\left(\mathrm{y}+5\right)\mathrm{yrs} \\ \mathrm{Now},\mathrm{y}+5=3\left(\mathrm{x}+5\right) \\ \Rightarrow \mathrm{y}+5=3\mathrm{x}+15 \\ \Rightarrow 3\mathrm{x}-\mathrm{y}=-10.....\left(1\right) \\ \mathbf{BEFORE}\mathbf{}\mathbf{5}\mathbf{}\mathbf{YEARS}\mathbf{}\mathbf{:} \\ \mathrm{son}\text{'}\mathrm{s}\mathrm{age}=\left(\mathrm{x}-5\right)\mathrm{yrs} \\ \mathrm{Father}\text{'}\mathrm{s}\mathrm{age}=\left(\mathrm{y}-5\right)\mathrm{yrs} \\ \mathrm{y}-5=7\left(\mathrm{x}-5\right) \\ \Rightarrow \mathrm{y}-5=7\mathrm{x}-35 \\ \Rightarrow 7\mathrm{x}-\mathrm{y}=30......\left(2\right) \\ \mathrm{Subtracting}\left(1\right)\mathrm{from}\left(2\right),\mathrm{we}\mathrm{get} \\ 4\mathrm{x}=40 \\ \Rightarrow \mathrm{x}=10 \\ \mathrm{Put}\mathrm{x}=10\mathrm{in}\left(1\right),\mathrm{we}\mathrm{get} \\ 30-\mathrm{y}=-10 \\ \Rightarrow \mathrm{y}=40 \\ \mathrm{So},\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{son}=10\mathrm{yrs} \\ \mathrm{Present}\mathrm{age}\mathrm{of}\mathrm{father}=40\mathrm{yrs} \end{gathered}$$