Up 20%, then down 20% — Percentages Aptitude Question
Up 20%, then down 20%: A price is increased by 20% and the new price is then decreased by 20%. Answer and worked solution on CodeKairo.
- Topic: Percentages
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 45 seconds
Question
A price is increased by 20% and the new price is then decreased by 20%. What is the net change from the original?
Options
- 4% decrease
- 2% decrease
- No change
- 4% increase
Show the answer and the worked solution
Correct answer: A. 4% decrease
Worked solution
- Take the original as 100. After +20%: 120. After −20% of 120: 120 − 24 = 96.
- Net change = 96 − 100 = −4, i.e. a 4% decrease.
Answer: 4% decrease.
The idea
Successive changes multiply: a% then b% gives a net of a + b + ab/100. An equal rise and fall of x% always nets to a loss of x²/100 percent — here 20²/100 = 4%.
Shortcut. Write it as (1 + 0.2)(1 − 0.2) = 1 − 0.2² = 0.96: a difference of squares, so an equal rise and fall always ends below the start.
Common trap. No change — assuming +20% and −20% cancel; the 20% cut is taken from the larger 120, so it removes 24.