Average of a group changes when one member leaves: A group of 10 friends has an average age of 15 years. One friend leaves and the new average of the remaining 9 becomes 16 years. Find the exact age of the friend who left.

Introduction / Context:This is a reverse-average problem: we know the overall mean before and after removing one value. Converting means to totals allows isolation of the missing age quickly.

Given Data / Assumptions:

• Initial group size = 10, average = 15 years
• After one leaves: size = 9, average = 16 years

Concept / Approach:Total = average * count. The difference between initial total and new total equals the age of the friend who left.

Step-by-Step Solution:

Verification / Alternative check:If the person who left was 6, the remainder totals 144 with 9 members, average 16, which matches the condition.

Why Other Options Are Wrong:

• 4, 5, 7, 8 years: do not produce the specified post-removal average.

Common Pitfalls:Confusing which total to subtract from which. The person who left equals initial total minus new total.

Final Answer:6 years