Scholarship holders in a ratio — Aptitude Question
Scholarship holders in a ratio: The ratio of boys to girls in a school is 3 : 2. If 20% of the boys and 25% of the… Answer and worked solution on CodeKairo.
- Topic: Ratio & Proportion
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
The ratio of boys to girls in a school is 3 : 2. If 20% of the boys and 25% of the girls hold scholarships, what percent of students do not hold one?
Options
- 72%
- 75%
- 78%
- 80%
Show the answer and the worked solution
Correct answer: C. 78%
Worked solution
- Boys = 3/5 = 60%, girls = 2/5 = 40%.
- Holders = 60% × 20% + 40% × 25% = 12% + 10% = 22%.
- Non-holders = 100% − 22% = 78%.
Answer: 78%.
The idea
Convert the ratio to percentages of the whole first, then apply each rate to its own group. Averaging 20% and 25% ignores the unequal group sizes.
Shortcut. Treat everyone at 20%, then add the girls' extra 5 points on their 40% share: 20% + 2% = 22% hold one, so 78% do not.
Common trap. "80%" — applying the boys' 20% to the whole school because boys are the majority, forgetting the girls' higher 25% rate.