The average age of Ram and Rahim is 18 years. The average age of Rahim and Ramesh is 25 years. The average age of Ram and Ramesh is 29 years. What is the age (in years) of the eldest of the three?

Let the ages of Ram, Rahim and Ramesh be $$x,y,z$$ respectively.

Average age of Ram and Rahim = 18 years

=> $$\frac{x+y}{2}=18$$

=> $$x+y=18\times2=36$$ -----------(i)

Similarly, $$y+z=25\times2=50$$ --------------(ii)

and $$x+z=29\times2=58$$ --------------(iii)

Adding equations (i),(ii) and (iii)

=> $$2(x+y+z)=36+50+58=144$$

=> $$x+y+z=\frac{144}{2}=72$$

Substituting value from equation (i) in above equation, we get :

=> $$z=72-36=36$$ years

Similarly, $$x=22$$ years and $$y=14$$ years

$$\therefore$$ Age of the eldest of the three = 36 years

=> Ans - (D)