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.
Aptitude
Average
Difficulty: Easy
Choose an option
Answer
Correct Answer: 74%
Explanation
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:
Total A = 20 * 80 = 1600Total B = 30 * 70 = 2100Combined total = 1600 + 2100 = 3700Combined average = 3700 / 50 = 74%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%