Two groups of candidates — Aptitude Question
Two groups of candidates: In an exam the average mark of passed candidates is 70 and of failed candidates 30. Answer and worked solution on CodeKairo.
- Topic: Mixtures & Alligation
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
In an exam the average mark of passed candidates is 70 and of failed candidates 30. The overall average is 60. What is the ratio of passed to failed candidates?
Options
- 1 : 3
- 3 : 1
- 2 : 1
- 1 : 2
Show the answer and the worked solution
Correct answer: B. 3 : 1
Worked solution
- Passed : failed = (60 − 30) : (70 − 60) = 30 : 10 = 3 : 1.
- Check: (3 × 70 + 1 × 30)/4 = 240/4 = 60. ✓
Answer: 3 : 1.
The idea
Each group's size is proportional to the other group's distance from the mean. The mean nearer 70 means more candidates passed.
Shortcut. The overall 60 sits nearer 70, so passed candidates outnumber failed ones — 3 : 1 or 2 : 1; 2 : 1 gives (140 + 30) ÷ 3 ≈ 56.7, so 3 : 1.
Common trap. "1 : 3" — pairing each group with its own distance from 60 instead of the other group's, which inverts the ratio.