The average of the present ages of Rajan and his son is 20 years. Rajan is three times as old as his son at present. What will be the age of Rajan after 5 years?

Introduction / Context:
This is a straightforward average and ratio based problem on ages. We are told the average age of a father and his son and also how many times the father is older than the son. From this information, we must calculate the father's present age and then determine his age after 5 years. Such questions are useful for practicing basic algebra and understanding how averages relate to sums.

Given Data / Assumptions:
- The average of the present ages of Rajan and his son is 20 years.
- Rajan is currently three times as old as his son.
- Ages are in complete years.
- We are asked to find Rajan's age 5 years from now.

Concept / Approach:
The average of two numbers is the sum of the numbers divided by 2. If the average of two ages is known, we can multiply the average by 2 to obtain the total of their ages. The condition that one person is three times as old as the other allows us to express their ages in terms of a single variable and solve a simple system of equations.

Step-by-Step Solution:
Step 1: Let the present age of the son be S years.Step 2: Rajan is three times as old as his son, so Rajan's present age is 3S years.Step 3: The average of their present ages is given as 20 years, so (S + 3S) / 2 = 20.Step 4: Simplify the numerator to get 4S / 2 = 20, which reduces to 2S = 20.Step 5: Divide both sides by 2 to obtain S = 10 years. Therefore, the son is 10 years old now.Step 6: Rajan's present age is 3S = 3 * 10 = 30 years.Step 7: After 5 years, Rajan's age will be 30 + 5 = 35 years.

Verification / Alternative check:
We can confirm the result by checking the average and the age multiple. Currently, the son is 10 years old and Rajan is 30 years old. The average age is (10 + 30) / 2 = 40 / 2 = 20 years, which matches the given average. Also, Rajan is 3 times as old as his son, because 30 = 3 * 10. After 5 years, Rajan will indeed be 35 years old. Everything is consistent.

Why Other Options Are Wrong:
If Rajan were 40, 28, 25, or 30 years old after 5 years, his current age would be 35, 23, 20, or 25 years respectively. None of these current ages, paired with a suitable son age, would satisfy both the given average of 20 years and the condition that the father is three times as old as the son. Only the value of 35 years after 5 years leads to a present age of 30 years and a son age of 10 years that meet all conditions.

Common Pitfalls:
Some learners mistakenly interpret the average as the age of each person instead of as a mean value. Others forget that both ages are included in the average and divide by the wrong number. Another error is to misapply the three times relation and write S = 3R instead of R = 3S. Writing the equations carefully and solving them step by step avoids these mistakes.

Final Answer:
Rajan will be 35 years old after 5 years.