A is 25% more than B — Percentages Aptitude Question
A is 25% more than B: If A's income is 25% more than B's, then B's income is what percent less than A's? Answer and worked solution on CodeKairo.
- Topic: Percentages
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 60 seconds
Question
If A's income is 25% more than B's, then B's income is what percent less than A's?
Options
- 16⅔%
- 20%
- 22%
- 25%
Show the answer and the worked solution
Correct answer: B. 20%
Worked solution
- Let B = 100, so A = 125.
- B falls short of A by 25, and as a fraction of A that is 25/125 = 1/5.
- So B is 20% less than A.
Answer: 20%.
The idea
If A is x% more than B, then B is 100x/(100 + x) percent less than A. The two percentages differ because they use different bases, and picking 100 for the base removes all the algebra.
Shortcut. 25% more = 1/4 more, so B = 4/5 of A — a fifth less, 20%. General rule: 1/n more ↔ 1/(n + 1) less.
Common trap. 25% — reusing the same percentage in reverse, though the gap of 25 is now measured against A's larger 125.