In an aptitude problem on ages, the average age of Ram and Rahim is 18 years, the average age of Rahim and Ramesh is 25 years, and the average age of Ram and Ramesh is 29 years. What is the age (in years) of the eldest among these three friends?

Introduction / Context:
This aptitude question on ages involves three people whose pairwise average ages are given. We are asked to determine the age of the eldest among them. Such questions test your ability to convert average information into total ages and then solve a simple system of linear equations.

Given Data / Assumptions:

- 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.
- All ages are in whole years and positive.

Concept / Approach:
Average age is defined as total age divided by the number of persons. For each pair, the average allows us to compute the sum of their ages. With three unknown ages and three equations coming from these sums, we can solve the system to obtain the individual ages of Ram, Rahim, and Ramesh. Finally, we identify the largest value to find the eldest person's age.

Step-by-Step Solution:
Step 1: Let the present ages of Ram, Rahim and Ramesh be R1, R2 and R3 years respectively. Step 2: From the first average, (R1 + R2) / 2 = 18 ⇒ R1 + R2 = 36. Step 3: From the second average, (R2 + R3) / 2 = 25 ⇒ R2 + R3 = 50. Step 4: From the third average, (R1 + R3) / 2 = 29 ⇒ R1 + R3 = 58. Step 5: Solve these equations. Subtract the first from the third: (R1 + R3) − (R1 + R2) = 58 − 36 ⇒ R3 − R2 = 22. Step 6: Use R2 + R3 = 50 and R3 − R2 = 22. Adding them gives 2R3 = 72 ⇒ R3 = 36 years. Step 7: Substitute back: R2 + 36 = 50 ⇒ R2 = 14 years. Step 8: From R1 + R2 = 36 ⇒ R1 + 14 = 36 ⇒ R1 = 22 years.

Verification / Alternative check:
Check each average: Ram and Rahim = (22 + 14) / 2 = 36 / 2 = 18 years, correct. Rahim and Ramesh = (14 + 36) / 2 = 50 / 2 = 25 years, correct. Ram and Ramesh = (22 + 36) / 2 = 58 / 2 = 29 years, correct. All the given conditions are satisfied by the ages 22, 14 and 36 years.

Why Other Options Are Wrong:
Ages such as 14 years, 22 years, 28 years or 40 years cannot be the eldest age because the system of equations forces Ramesh to be 36 years old. No other value is consistent with all three pairwise averages at the same time.

Common Pitfalls:
Students sometimes treat the given averages as individual ages or forget to convert them into sums correctly. Another error is attempting to guess and check values rather than solving systematically. Always remember that average × number of persons = total age, and use that to set up clean algebraic equations.

Final Answer:
The eldest among the three is 36 years old.