Average weight rises when two women are replaced by two men: The average weight of 10 women increases by 1 kg when two women weighing 42 kg and 38 kg are replaced by two men. What is the average weight of the two men (in kg)?

Introduction / Context:
Replacing members in an average changes the total. If the average for 10 people rises by 1 kg, the total rises by 10 kg. That total rise must equal the difference between the men’s combined weight and the two women’s combined weight.

Given Data / Assumptions:

• n = 10; average increases by 1 kg → total increases by 10 kg
• Women replaced: 42 kg and 38 kg (sum = 80 kg)
• Let men’s combined weight = M

Concept / Approach:
M − 80 = 10 → M = 90. Average weight of the two men is M / 2.

Step-by-Step Solution:
Increase in total = 10 kgM − 80 = 10 → M = 90 kgMen’s average = 90 / 2 = 45 kg

Verification / Alternative check:
Replacing 80 kg by 90 kg increases the 10-person total by 10, making the average rise by 1 kg, exactly as stated.

Why Other Options Are Wrong:
46, 44, 42, 47 kg do not match the required 10 kg increase in the 10-person total.

Common Pitfalls:
Using the original average (unknown) or dividing the 10 kg rise by 2 erroneously without first adding back the replaced weights. Compute combined totals first.

Final Answer:
45kg