Question

​​present age of father is 3 more than 3 times his sons age. after 10 years father will be 10 more than twice his sons age. find their present ages

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{son}=\mathrm{x}\mathrm{yrs} \\ \mathrm{Present}\mathrm{age}\mathrm{of}\mathrm{father}=\left(3\mathrm{x}+3\right)\mathrm{yrs} \\ \mathbf{AFTER}\mathbf{}\mathbf{10}\mathbf{}\mathbf{YEARS}\mathbf{}: \\ \mathrm{son}\text{'}\mathrm{s}\mathrm{age}=\left(\mathrm{x}+10\right)\mathrm{yrs} \\ \mathrm{Father}\text{'}\mathrm{s}\mathrm{age}=\left(3\mathrm{x}+3+10\right)\mathrm{yrs}=\left(3\mathrm{x}+13\right)\mathrm{yrs} \\ \mathrm{Now},\mathrm{according}\mathrm{to}\mathrm{question}: \\ 3\mathrm{x}+13=2\left(\mathrm{x}+10\right)+10 \\ \Rightarrow 3\mathrm{x}+13=2\mathrm{x}+20+10 \\ \Rightarrow 3\mathrm{x}+13=2\mathrm{x}+30 \\ \Rightarrow 3\mathrm{x}-2\mathrm{x}=30-13 \\ \Rightarrow \mathrm{x}=17 \\ \mathrm{So},\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{son}=17\mathrm{yrs} \\ \mathrm{Present}\mathrm{age}\mathrm{of}\mathrm{father}=17\times 3+3=54\mathrm{yrs} \end{gathered}$$