Finding boys from overall and subgroup means: In a class of 150 students, the overall mean weight is 60 kg. The mean weight of boys is 70 kg and that of girls is 55 kg. How many boys are there?

Introduction / Context:
This is a standard two-group weighted average problem. The overall mean equals the weighted sum of subgroup means divided by the total count; solving yields the subgroup size.

Given Data / Assumptions:

• Total n = 150; overall mean = 60
• Boys’ mean = 70; Girls’ mean = 55
• Let number of boys = b, girls = 150 − b

Concept / Approach:
(70b + 55(150 − b)) / 150 = 60. Solve for b.

Step-by-Step Solution:
(70b + 8250 − 55b) / 150 = 60(15b + 8250) = 900015b = 750 → b = 50

Verification / Alternative check:
Totals: boys 50 * 70 = 3500; girls 100 * 55 = 5500; combined 9000 / 150 = 60 matches overall mean.

Why Other Options Are Wrong:
60, 75, 90, 100 do not satisfy the weighted-average equation.

Common Pitfalls:
Swapping subgroup sizes or forgetting to weight means by their counts.

Final Answer:
50