Question

The sum of present ages of John and his father is 89 years. After 11 yrs the age of father will be twice the age of John at that time, find their present ages.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{John}=\mathrm{x}\mathrm{yrs} \\ \mathrm{Let}\mathrm{the}\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{father}=\mathrm{y}\mathrm{yrs} \\ \mathrm{Now},\mathrm{according}\mathrm{to}\mathrm{first}\mathrm{condition}: \\ \mathrm{x}+\mathrm{y}=89.....\left(1\right) \\ \mathbf{After}\mathbf{}\mathbf{11}\mathbf{}\mathbf{years}\mathbf{}\mathbf{:} \\ \mathrm{John}\text{'}\mathrm{s}\mathrm{age}=\left(\mathrm{x}+11\right)\mathrm{yrs} \\ \mathrm{Father}\text{'}\mathrm{s}\mathrm{age}=\left(\mathrm{y}+11\right)\mathrm{yrs} \\ \mathrm{Now},\mathrm{according}\mathrm{to}\mathrm{second}\mathrm{condition}: \\ \mathrm{y}+11=2\left(\mathrm{x}+11\right) \\ \Rightarrow \mathrm{y}+11=2\mathrm{x}+22 \\ \Rightarrow 2\mathrm{x}-\mathrm{y}=-11.....\left(2\right) \\ \mathrm{Adding}\left(1\right)\mathrm{and}\left(2\right),\mathrm{we}\mathrm{get} \\ 3\mathrm{x}=78 \\ \Rightarrow \mathrm{x}=26 \\ \mathrm{Now},\mathrm{from}\left(1\right),\mathrm{we}\mathrm{get} \\ 26+\mathrm{y}=89 \\ \Rightarrow \mathrm{y}=63 \\ \mathrm{So},\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{John}=26\mathrm{yrs} \\ \mathrm{Present}\mathrm{age}\mathrm{of}\mathrm{father}=63\mathrm{yrs} \end{gathered}$$