Solution

Let Rakesh's age = \( R \), Mahesh's age = \( M \)

Given: \( R + M = 60 \)

From the statement:
Rakesh says, "I am as old as you were when I was one-third as old as you are"

That is, when Rakesh was \( \frac{1}{3}M \), Mahesh's age was \( R \)
So, time passed = \( R - \frac{1}{3}M \)
Then Mahesh's age was: \( M - (R - \frac{1}{3}M) = R \)

Now solve the equation:

\( M - (R - \frac{1}{3}M) = R \)
\( M - R + \frac{1}{3}M = R \)
\( \frac{4}{3}M = 2R \)
\( 4M = 6R \Rightarrow 2M = 3R \Rightarrow M = \frac{3}{2}R \)

Now plug into \( R + M = 60 \)
\( R + \frac{3}{2}R = 60 \Rightarrow \frac{5}{2}R = 60 \Rightarrow R = 24 \)
\( M = \frac{3}{2} \times 24 = 36 \)