A salary up 20%, then down 20% — Aptitude Question
A salary up 20%, then down 20%: A salary is increased by 20% and the new figure is then decreased by 20%. Answer and worked solution on CodeKairo.
- Topic: Percentages
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 45 seconds
Question
A salary is increased by 20% and the new figure is then decreased by 20%. What is the net change?
Options
- 4% decrease
- No change
- 2% increase
- 4% increase
Show the answer and the worked solution
Correct answer: A. 4% decrease
Worked solution
- Take the salary as 100. After +20%: 120.
- After −20% of 120: 120 − 24 = 96.
- Net change = −4, a 4% decrease.
Answer: 4% decrease.
The idea
An equal rise and fall of x% always ends in a net loss of x²/100 percent. Chaining multipliers (1.2 × 0.8 = 0.96) is the reliable way to see it.
Shortcut. (1 + 0.2)(1 − 0.2) = 1 − 0.2² = 0.96 by the difference of squares, so the salary ends 4% lower — a decrease whatever the order.
Common trap. "No change" — letting +20% and −20% cancel, forgetting the cut is taken on the raised 120, not the original 100.