The price of a storybook was $80. It increased by 20% and then decreased by 25%. Which of the following statements is correct?
- The final price is the same as the original price.
- The final price is 10% lower than the original price.
- The final price is 10% higher than the original price.
- The final price is 25% lower than the original price.
Need a hint?
Find the new price after the 20% increase first. Then take the 25% decrease from that new price, not from $80.
Worked answer
- Original price = $80.
- After a 20% increase: 80 × 1.2 = $96.
- After a 25% decrease of the new price $96: 25% of 96 = $24, so the final price = 96 − 24 = $72.
- Compare with the original: 80 − 72 = $8, and 8 ÷ 80 = 10%, so the final price is 10% lower than the original.
Answer: The final price is 10% lower than the original price.
The mistake this question tests
Habit
Found the increase, not the new price
Many pupils take the 25% decrease from the original $80 (giving $60), or assume the two changes cancel out. The second percentage must be applied to the price after the first change.
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