Pass–fail split via averages: The average of 120 students is 35. If those who passed averaged 39 and those who failed averaged 15, how many students passed?

Introduction / Context:
This classic mixture problem uses subgroup averages and the overall average to find subgroup sizes. Convert averages to totals and form a simple linear equation in the number of passed students.

Given Data / Assumptions:

• Total students = 120
• Overall average = 35
• Average (passed) = 39
• Average (failed) = 15

Concept / Approach:
Let the number of students who passed be x. Then total marks = 39x + 15(120 - x). Equate this to the overall total 120 * 35 and solve for x.

Step-by-Step Solution:

Verification / Alternative check:
Compute totals: passed = 100 * 39 = 3900; failed = 20 * 15 = 300; sum = 4200, which matches the overall requirement.

Why Other Options Are Wrong:

• 80, 92, 88, 96: do not satisfy the balance of subgroup totals to 4200.

Common Pitfalls:
Forgetting that the failed group size is 120 - x or mis-multiplying the subgroup totals.

Final Answer:
100