The average age of Rustam and Preetam is 39 years. The average age of Preetam and Geetam is 28 years. The average age of Rustam and Geetam is 34 years. What will be the age (in years) of the youngest of the three after 10 years?

Let respective ages of Rustam, Preetam and Geetam be $$r,p,g$$ years

Average age of Rustam and Preetam = 39 years

=> $$\frac{r+p}{2}=39$$

=> $$r+p=78$$ ----------(i)

Similarly, $$p+g=56$$ ----------(iii)

and $$r+g=68$$ ------------(iii)

Adding all the equations, we get :

=> $$2(r+p+g)=78+56+68$$

=> $$r+p+g=\frac{202}{2}=101$$ ------------(iv)

Substituting value from equation (i) in equation (iv),

=> $$78+g=101$$

=> $$g=101-78=23$$ years

Similarly, $$r=45$$ years and $$p=33$$ years

$$\therefore$$ Age (in years) of the youngest, i.e. Gautam after 10 years = $$23+10=33$$ years

=> Ans - (C)