16Hit 1600
Problem-Solving and Data AnalysisVery hardReversing a chain of percent changes

Problem-Solving and Data Analysis practice question

The regular price of a bicycle at a shop was increased by 25%. Later, during a sale, this increased price was reduced by p%, and the resulting sale price was 10% less than the regular price had been before the increase. What is the value of p?

Answer: 28

Let the original regular price be 100 dollars. After the 25% increase, the price is 125 dollars. The sale price must be 10% less than 100, or 90 dollars. The reduction is 125 − 90 = 35 dollars, and this reduction is taken off the increased price, so p = 35/125 × 100 = 28. Common wrong answers: 35, which comes from expressing the 35-dollar reduction as a percent of the original 100 dollars instead of the increased 125 dollars; 15, from subtracting the percents (25 − 10) as if percent changes applied to the same base; and 12.5, from assuming the price must simply return partway to 100 without accounting for the 10% drop correctly.

Common wrong answers

If you answered 15
You subtracted 25 − 10, but percent changes apply to different bases — the 25% is on $100 and p% is on $125.
If you answered 35
The $35 reduction is correct, but you took it as a percent of the original $100; the discount comes off the increased price, so p = 35/125 × 100 = 28.
If you answered 12.5
That percent brings $125 back partway toward $100 rather than down to $90; the sale price must be 10% below the original.

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