Pass rates in two sections — Caselets Aptitude Question
Pass rates in two sections: Section A has 50 students of whom 80% passed. Section B has 30 students of whom 60%… Answer and worked solution on CodeKairo.
- Topic: Caselets
- Section: Data Interpretation
- Difficulty: Medium
- Time target: 75 seconds
Question
Section A has 50 students of whom 80% passed. Section B has 30 students of whom 60% passed.
What is the overall pass percentage across both sections?
Options
- 70%
- 72.5%
- 75%
- 77.5%
Show the answer and the worked solution
Correct answer: B. 72.5%
Worked solution
- Section A passes = 80% of 50 = 40. Section B passes = 60% of 30 = 18.
- Total passes = 58 out of 80 students.
- Overall = 58/80 × 100 = 72.5%.
Answer: 72.5%.
The idea
An overall percentage is total favourable ÷ total, never the average of two percentages. The simple average of 80 and 60 gives 70, which is offered here precisely because it is wrong.
Shortcut. The sections weigh 50 : 30 = 5 : 3, so the overall rate lies 3/8 of the way from 80 towards 60: 80 − 20 × 3/8 = 80 − 7.5 = 72.5%.
Common trap. 70% is the plain average of 80% and 60%, which ignores that Section A has 50 students against B's 30 and so counts for more.