Question

Father is 7 times as old as his son .10 years later he will be three times as old as his son. find their ages

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{son}\mathrm{be}\mathrm{x}\mathrm{years} \\ \mathrm{Then}\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{father}\mathrm{will}\mathrm{be}7\mathrm{x}\mathrm{years} \\ \mathrm{After}10\mathrm{years} \\ \mathrm{Son}\text{'}\mathrm{s}\mathrm{age}=(\mathrm{x}+10)\mathrm{years} \\ \mathrm{Father}\text{'}\mathrm{s}\mathrm{age}=(7\mathrm{x}+10)\mathrm{years} \\ \mathrm{ATQ}. \\ \mathrm{Father}\text{'}\mathrm{s}\mathrm{age}=3\times \mathrm{Son}\text{'}\mathrm{s}\mathrm{age} \\ \Rightarrow 7\mathrm{x}+10=3(\mathrm{x}+10) \\ \Rightarrow 7\mathrm{x}+10=3\mathrm{x}+30 \\ \Rightarrow 4\mathrm{x}=20 \\ \Rightarrow \mathrm{x}=5 \\ \mathrm{So},\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{son}=5\mathrm{years} \\ \mathrm{present}\mathrm{age}\mathrm{of}\mathrm{father}=7\left(5\right)=35\mathrm{years} \end{gathered}$$