Why a 20% Increase and 20% Decrease Do Not Cancel

A twenty percent increase followed by a twenty percent decrease does not restore the original price. Each change uses the current price as its base.

Start with one hundred dollars. A twenty percent increase multiplies it by one point two, giving one hundred twenty dollars. The next decrease starts from that larger price.

A twenty percent decrease multiplies one hundred twenty by zero point eight, leaving ninety six dollars. The combined multiplier is zero point nine six: ninety six percent of the original, a four percent decrease.

For a twenty five percent increase followed by a ten percent decrease, multiply one point two five by zero point nine. The result is one point one two five, or one hundred twelve point five percent of the original.

The first change gives 100 × 1.20 = 120. The second gives 120 × 0.80 = 96. The net percentage change is (96 − 100)/100 × 100% = −4%. The generalized multiplier 1.20 × 0.80 = 0.96 confirms the same result for any positive original price.

A price increases by 25% and then decreases by 10%. What percentage of the original price remains?

Answer: 112.5%. The combined multiplier is 1.25 × 0.90 = 1.125. Starting with $100 checks this independently: $125 then $112.50. The net increase is 12.5%.

Read the full worked question for answer choices, distractor explanations and another method. These are original PeakSAT teaching examples with Google-generated narration, not official SAT questions or score predictions.