Percents don't simply cancel.
Up 20%, then down 20%
An original website mini lesson · Learning On My Own
The trap
A price goes up 20%, then down 20%. Many people say "back where it started". It isn't, because the second 20% is taken from a bigger number.
Start at 100
- Up 20%: 100 × 1.2 = 120.
- Down 20% of 120 is 24: 120 − 24 = 96.
- The price ends 4% lower than it started.
The method that always works
Turn each change into a multiplier, then multiply them. Up 20% is × 1.2. Down 20% is × 0.8. Together: 1.2 × 0.8 = 0.96, which means 4% down. No starting number needed, so it is fast under the clock.
Two rises add up to more than you'd expect too: up 10% twice is 1.1 × 1.1 = 1.21, a 21% rise, not 20%.
Your turn
A price rises 25%, then falls 20%. Is it higher, lower or the same as at the start?
See the answer and reason
1.25 × 0.8 = 1, so it is exactly the same. A 20% fall undoes a 25% rise, because 20% of the bigger number equals 25% of the smaller one.
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