A is 20% less than B — Percentages Aptitude Question
A is 20% less than B: If A's income is 20% less than B's, then B's income is what percent more 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 20% less than B's, then B's income is what percent more than A's?
Options
- 20%
- 22.5%
- 25%
- 30%
Show the answer and the worked solution
Correct answer: C. 25%
Worked solution
- Let B = 100, so A = 80.
- B exceeds A by 20, and as a fraction of A that is 20/80 = 1/4.
- So B is 25% more than A.
Answer: 25%.
The idea
If A is x% less than B, then B is 100x/(100 − x) percent more than A. Note the minus sign: a fall of 20% needs a rise of 25% to undo it.
Shortcut. 20% less = 1/5 less, so B = 5/4 of A — a quarter more, 25%. General rule: 1/n less ↔ 1/(n − 1) more.
Common trap. 20% — assuming the percentage works the same in both directions, though the gap of 20 is measured against the smaller 80.