SAT Percentages: An Increase Followed by a Decrease

A price increases by 20% and then decreases by 20% of the increased price. What percentage of the original price is the final price?

Express the increase as a multiplier

Let the original price be p. Increasing by 20% gives 1.20p.

Apply the decrease to the new base

A 20% decrease multiplies the increased price by 0.80, so the final price is 0.80(1.20p) = 0.96p.

Translate the multiplier

A multiplier of 0.96 means the final price is 96% of the original. This is a net decrease of 4%.

Choose an original price of $100. It becomes $120, then loses 20% of $120, or $24. The final $96 is 96% of $100. Using $100 is valid because the question asks for a ratio, not a specific starting price.

• 80% applies the decrease without first applying the increase.
• 100% incorrectly cancels rates computed on different bases.
• 104% reverses the direction of the actual net change.

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

Answer: 112.5%

1.25 × 0.90 = 1.125, so the result is 112.5% of the original.

If this was difficult, return to percentages practice and identify the precise step to improve. These are original PeakSAT teaching examples, not official College Board questions or calibrated score predictions. For official adaptive test practice, use Bluebook (opens in a new tab).