Passed candidates from overall average: Among 120 candidates, the overall average marks are 35. Passed candidates average 39, and failed candidates average 15. How many candidates passed?

Introduction / Context:
Classic two-group mixture: express grand total via overall average and equate it to the sum of group totals from their averages to solve the passed count.

Given Data / Assumptions:

• Total candidates = 120; overall average = 35 ⇒ total marks = 4200.
• Passed average = 39; Failed average = 15.

Concept / Approach:
Let p be the number passed. Then 39p + 15(120 − p) = 4200. Solve for p.

Step-by-Step Solution:

Verification / Alternative check:
Totals: pass = 3900; fail = 20*15 = 300; sum = 4200; average = 4200/120 = 35. All consistent.

Why Other Options Are Wrong:

• 110, 120, 150: Do not satisfy the weighted-average equation with given group means.

Common Pitfalls:
Attempting to average the group averages without weighting by counts leads to wrong answers.

Final Answer: