Pass–fail composition: The average of 120 students is 30. Passed students average 40 and failed students average 10. What is 25% of the number of passed students?

Introduction / Context:
Convert overall and subgroup averages to totals to find the number who passed. Once the passed count is known, take one quarter (25%) as requested.

Given Data / Assumptions:

• Total students = 120
• Overall average = 30 → total = 3600
• Passed average = 40
• Failed average = 10

Concept / Approach:
Let x be the number who passed. Then 40x + 10(120 - x) = 3600. Solve for x, then compute 0.25x.

Step-by-Step Solution:

Verification / Alternative check:
Totals: passed = 80 * 40 = 3200; failed = 40 * 10 = 400; sum = 3600, consistent with the overall total.

Why Other Options Are Wrong:

• 30, 40, 15, 25: not equal to one quarter of 80.

Common Pitfalls:
Using an unweighted average or forgetting to subtract x when computing the failed count 120 - x.

Final Answer:
20