Question

Monu's father is 26 years younger than Monu's grandfather and 29 years older than Monu. The sum of the ages of all the three is 135 years. What is the age of each one of them?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{age}\mathrm{of}\mathrm{Monu}\text{'}\mathrm{s}\mathrm{father}\mathrm{be}\mathrm{x}\mathrm{years}. \\ \mathrm{The}\mathrm{age}\mathrm{of}\mathrm{Monu}\text{'}\mathrm{s}\mathrm{grandfather}\mathrm{will}\mathrm{be}(\mathrm{x}+26). \\ \mathrm{Then},\mathrm{the}\mathrm{age}\mathrm{of}\mathrm{Monu}\mathrm{will}\mathrm{be}(\mathrm{x}-29). \\ \therefore x+(x+26)+(x-29)=135 \\ \Rightarrow x+x+26+x-29=135 \\ \Rightarrow 3x-3=135 \\ \Rightarrow 3x=135+3 \\ \Rightarrow 3x=138 \\ \Rightarrow x=\frac{138}{3}=46 \\ \therefore A\mathrm{ge}\mathrm{of}\mathrm{Monu}\text{'}\mathrm{s}\mathrm{father}=46\mathrm{years} \\ \mathrm{Age}\mathrm{of}\mathrm{Monu}\text{'}\mathrm{s}\mathrm{grandfather}=(\mathrm{x}+26)=(46+26)=72\mathrm{years} \\ \mathrm{Age}\mathrm{of}\mathrm{Monu}=(\mathrm{x}-29)=46-29=17\mathrm{years} \end{gathered}$$