Question

Sum of ages of father and son is 40years. If dather's age is 3times that of his son,then find their respective ages

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{age}\mathrm{of}\mathrm{son}=\mathrm{x}\mathrm{yrs} \\ \mathrm{Let}\mathrm{the}\mathrm{age}\mathrm{of}\mathrm{father}=\mathrm{y}\mathrm{yrs} \\ \mathrm{Now},\mathrm{according}\mathrm{to}\mathrm{first}\mathrm{condition}: \\ \mathrm{x}+\mathrm{y}=40.........\left(1\right) \\ \mathrm{Now},\mathrm{according}\mathrm{to}\mathrm{second}\mathrm{condition}: \\ \mathrm{y}=3\mathrm{x}.......\left(2\right) \\ \mathrm{Substitute}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{y}\mathrm{from}\left(2\right)\mathrm{in}\left(1\right),\mathrm{we}\mathrm{get} \\ \mathrm{x}+3\mathrm{x}=40 \\ \Rightarrow 4\mathrm{x}=40 \\ \Rightarrow \mathrm{x}=\frac{40}{4}=10 \\ \mathrm{Put}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{x}\mathrm{in}\left(2\right),\mathrm{we}\mathrm{get} \\ \mathrm{y}=3\times 10=30 \\ \mathrm{So},\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{son}=10\mathrm{yrs} \\ \mathrm{Present}\mathrm{age}\mathrm{of}\mathrm{father}=30\mathrm{yrs} \end{gathered}$$
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