Pass–fail split from overall average: In a class of 80 students, overall average marks are 40. Passed students average 60 and failed students average 35. How many students failed?

Introduction / Context:
Mixture-averages with two groups can be solved by equating weighted totals. Let p pass and 80 - p fail; use the given group averages to match the overall total.

Given Data / Assumptions:

• Total students = 80; overall average = 40 ⇒ total marks = 3200.
• Passed average = 60; Failed average = 35.

Concept / Approach:
Total = (pass count * pass avg) + (fail count * fail avg). Solve for p, then compute failed = 80 - p.

Step-by-Step Solution:

Verification / Alternative check:
Totals: 16*60 = 960; 64*35 = 2240; sum = 3200, average = 3200/80 = 40. Correct.

Why Other Options Are Wrong:

• 63, 60, 72: Do not satisfy the weighted-total equation with the given averages.

Common Pitfalls:
Confusing pass and fail counts or forgetting to multiply averages by their respective counts.

Final Answer: