Replacement effect on average weight: The average weight of 8 men rises by 2 kg when a 50 kg man is replaced by a newcomer. What is the newcomer’s weight?

Introduction / Context:
When a replacement raises the average by a known amount, the total for the group rises by (group size * rise in average). Add this increase to the departing member’s weight to get the newcomer’s weight.

Given Data / Assumptions:

• Group size = 8 men.
• Average increase = 2 kg.
• Departing weight = 50 kg.

Concept / Approach:
Total increase = group size * increase in average. Newcomer = departing + total increase (since only one person changed).

Step-by-Step Solution:

Verification / Alternative check:
Let old total be T. New total must be T - 50 + 66 = T + 16; average rises by 16/8 = 2, as stated.

Why Other Options Are Wrong:

• 52, 58: Too small; would not raise the average by 2.
• 68: Would raise the total by 18, hence average by 2.25, not 2.

Common Pitfalls:
Multiplying the average increase by 7 (excluding the replaced person) instead of the full group count 8.

Final Answer: