Section-wise pass averages: Section A has 20 students with an average of 80%. Section B has 30 students with an average of 70%. Find the combined passing average of all 50 students.

Introduction / Context:
Combining two groups with different averages requires a weighted mean using their sizes. Larger groups influence the result more than smaller groups.

Given Data / Assumptions:

• Section A: 20 students, average 80%
• Section B: 30 students, average 70%

Concept / Approach:
Combined average = (sum of group totals) / (total students). Compute each total as average * size and divide by 50.

Step-by-Step Solution:

Verification / Alternative check:
The combined mean must lie between 70% and 80% and be closer to 70% since the larger group (30) is at 70%. 74% fits that intuition.

Why Other Options Are Wrong:

• 72%, 75%, 77%, 73%: do not equal 3700/50.

Common Pitfalls:
Averaging 80 and 70 directly to 75% ignores group sizes and leads to an incorrect result here.

Final Answer:
74%