If a price has already been increased or decreased, you can find the original by dividing by the multiplier. After a 10% rise, the new amount is 110% of the original, so original = new ÷ 1.10.
Tom's pay after a 10% rise is $104.50, so before the rise it was 104.50 ÷ 1.1 = $95. A common mistake is to take 10% off the new amount, which gives the wrong answer because 10% of the new amount is bigger than 10% of the original.
Worked example
A car's price is reduced by 15% to $8500. What was the original price?
- The sale price is 85% of the original: multiplier 0.85.
- 8500 ÷ 0.85 = 10 000.
Answer:$10 000
Key words
- original
- the amount before the change
- reverse percentage
- working back to the original
- multiplier
- 1 ± the percentage as a decimal
Practise this
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