Question

The sum of the present ages of Ram and Mohan is 60 years. In 8 years Ram will be 5 years older than three times as old as Mohan was three years ago. Find their Present Ages.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{Ram}=x\mathrm{yrs} \\ \mathrm{Let}\mathrm{the}\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{Mohan}=y\mathrm{yrs} \\ \mathrm{Now} \\ x+y=60......\left(1\right) \\ \left(x+8\right)=3\left(y-3\right)+5 \\ \Rightarrow x+8=3y-9+5 \\ \Rightarrow x-3y=-12......\left(2\right) \\ \mathrm{Subtracting}\left(2\right)\mathrm{from}\left(1\right),\mathrm{we}\mathrm{get} \\ 4y=72 \\ \Rightarrow y=18 \\ \mathrm{Now},\mathrm{from}\left(1\right),\mathrm{we}\mathrm{get} \\ x+18=60 \\ \Rightarrow x=60-18=42 \\ \mathrm{So},\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{Ram}=42\mathrm{yrs} \\ \mathrm{present}\mathrm{age}\mathrm{of}\mathrm{Mohan}=18\mathrm{yrs} \end{gathered}$$