Passing in both subjects — Percentages Aptitude Question
Passing in both subjects: In an examination 35% failed in Mathematics, 45% failed in English and 20% failed in both. Answer and worked solution on CodeKairo.
- Topic: Percentages
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 60 seconds
Question
In an examination 35% failed in Mathematics, 45% failed in English and 20% failed in both. What percent passed in both subjects?
Options
- 20%
- 30%
- 40%
- 45%
Show the answer and the worked solution
Correct answer: C. 40%
Worked solution
- Failed in at least one = 35% + 45% − 20% = 60%.
- Passed in both = 100% − 60% = 40%.
Answer: 40%.
The idea
Subtract the overlap once when adding two groups, then take the complement. Adding 35 and 45 without removing the 20 counted twice gives 20%, which is offered.
Shortcut. Passed both = 100 − 35 − 45 + 20 = 40%: the two failure figures subtract the 'failed both' group twice, so add it back once.
Common trap. 20% — subtracting both failure rates (35 + 45 = 80) from 100 without adding back the 20% counted twice.