Question

I'm currently 5 times as old as my son. In 6 years time I will be three times as old as he will be then. What are our ages now?

Answer 1

Dear student
$$\begin{gathered} \mathrm{Let}\mathrm{son}\text{'}\mathrm{s}\mathrm{age}\mathrm{be}\mathrm{x}\mathrm{years} \\ \mathrm{Then}\mathrm{father}\text{'}\mathrm{s}\mathrm{age}=5\mathrm{x}\mathrm{years} \\ \mathrm{Afetr}\mathrm{six}\mathrm{years} \\ \mathrm{Son}\text{'}\mathrm{s}\mathrm{age}=\left(\mathrm{x}+6\right)\mathrm{years} \\ \mathrm{father}\text{'}\mathrm{s}\mathrm{age}=\left(5\mathrm{x}+6\right)\mathrm{years} \\ \mathrm{According}\mathrm{to}\mathrm{question} \\ 5\mathrm{x}+6=3(\mathrm{x}+6) \\ \Rightarrow 5\mathrm{x}+6=3\mathrm{x}+18 \\ \Rightarrow 2\mathrm{x}=12 \\ \Rightarrow \mathrm{x}=6 \\ \mathrm{So},\mathrm{son}\text{'}\mathrm{s}\mathrm{present}\mathrm{age}=6\mathrm{years} \\ \mathrm{and}\mathrm{father}\text{'}\mathrm{s}\mathrm{present}\mathrm{age}=5\times 6=30\mathrm{years} \end{gathered}$$
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