The average age of a 5-member committee today is the same as it was 3 years ago because one old member was replaced by a new member. What is the difference between the ages of the old and the new member?

Introduction:
If a group’s average remains unchanged after a certain number of years despite everyone aging, then the replacement must have offset exactly the total aging of the group. This insight allows a quick computation of the difference between the outgoing and incoming member’s ages.

Given Data / Assumptions:

• Committee size remains 5
• Average now equals average 3 years ago
• One old member replaced by one new member

Concept / Approach:
If no one were replaced, the total age would increase by 5 * 3 = 15 years over 3 years. Since the average (and thus total) is unchanged, the incoming member must be younger than the outgoing member by exactly 15 years to cancel out this increase.

Step-by-Step Solution:

Verification / Alternative check:
Model totals numerically: if old total was S, after 3 years without replacement it would be S + 15. With replacement, it returns to S, implying a 15-year reduction due to replacement, i.e., the age gap is 15.

Why Other Options Are Wrong:
2, 4, 8, and 10 years would not offset the full 15-year increase across five members over three years.

Common Pitfalls:
Multiplying by 3 only once or forgetting to apply it to all 5 members. The average constraint fixes the exact difference.

Final Answer:
15 years