The sum of the present ages of Ram and his son is 48 years. If Ram's uncle's age is also included, the average of their ages (Ram, his son and his uncle) becomes 40 years. What is the age (in years) of Ram's uncle?

Introduction / Context:
This question tests your understanding of averages and how adding a new person affects the average age. We know the combined age of Ram and his son, and we are told what happens to the average when Ram's uncle is included. From this information, we must determine the uncle's present age.

Given Data / Assumptions:

- The sum of the present ages of Ram and his son is 48 years.
- When Ram's uncle is also included, the average age of all three (Ram, his son and his uncle) is 40 years.
- We must find the uncle's present age in years.

Concept / Approach:
Average age is total age divided by number of persons. The total age of Ram and his son is known directly. When we include the uncle and use the new average, we can compute the new total age for the three persons. The uncle's age is then obtained by subtracting the combined age of Ram and his son from this new total. This is a simple application of the formula total = average × number of persons.

Step-by-Step Solution:
Step 1: Let Ram's present age be R years and his son's present age be S years. Step 2: It is given that R + S = 48 years. Step 3: When Ram's uncle is included, there are 3 persons in total. Step 4: The average age of these three persons is 40 years. Step 5: Therefore, total age of Ram, his son and his uncle together = 3 × 40 = 120 years. Step 6: Let the uncle's present age be U years. Then R + S + U = 120. Step 7: Substitute R + S = 48 to get 48 + U = 120. Step 8: Solve for U: U = 120 − 48 = 72 years.

Verification / Alternative check:
If the uncle is 72 years old, then the total age of the three is 48 + 72 = 120 years. Dividing 120 by 3 gives an average age of 40 years, which matches the condition in the question. This confirms that the uncle's present age is correctly calculated as 72 years.

Why Other Options Are Wrong:
Ages such as 34, 48, 50 or 60 years for the uncle would lead to total ages of 82, 96, 98 or 108 years respectively when added to 48, giving averages different from 40 years for 3 persons. Only 72 years produces the exact average of 40 years required by the question.

Common Pitfalls:
Some students wrongly average the known total of 48 with 40, or attempt to treat 40 as another age instead of an average. Others may forget that the new average applies to 3 people, not 2. Always convert averages into totals using total = average × number of persons before comparing or subtracting ages.

Final Answer:
Ram's uncle is 72 years old.