Question

Rakesh says to Mahesh, "I am as old as you were when I was one-third as old as you are". If the sum of their ages is 60 years, find the present age of Mahesh (in years).

• A. 45
• B. 36
• C. 30
• D. 24

Hint:

When solving age-related word problems, set up equations based on the given conditions and solve step by step.

Answer 1

The Correct Option is B

Let the present age of Rakesh be \( r \) years, and the present age of Mahesh be \( m \) years.
We are given the following:
- The sum of their ages is 60, i.e., \[ r + m = 60 \]
- Rakesh says, "I am as old as you were when I was one-third as old as you are." This means: \[ r = m - \left( \frac{r}{3} \right) \]
Now substitute \( r = 60 - m \) from the first equation into the second equation:
\[ 60 - m = m - \left( \frac{60 - m}{3} \right) \] Multiply through by 3 to eliminate the fraction:
\[ 3(60 - m) = 3m - (60 - m) \] \[ 180 - 3m = 3m - 60 + m \] Simplifying:
\[ 180 - 3m = 4m - 60 \] \[ 180 + 60 = 4m + 3m \] \[ 240 = 7m \] \[ m = \frac{240}{7} \approx 36 \] Thus, Mahesh's present age is \( \boxed{36} \) years.