Keep the original as 100%
A percentage increase or decrease uses the original value as its base. That original is 100%.
A 20% increase gives 120% of the original. A 20% decrease leaves 80%. To go backwards, divide by the final proportion.
Divide by the new proportion
96 ÷ 1.2 = 80
80 + 16 = 96
After a 20% increase, a value is 96. That 96 is 120% of the original, so divide by 1.2 to find 80.
Check it: 20% of 80 is 16, and 80 + 16 = 96.
Subtracting 20% of 96 would give 76.8. That uses 96 as the base, so it does not undo the original increase.
Find a price before a discount
After a 25% discount, a price is 54. What was the price before the discount?
The 54 is 75% of the original price. Divide by 0.75 to recover 100%.
Try it
What was the original price before the 25% discount?
- 67.50
- 72
Show the answer
72
The discounted price is 75% of the original: 54 ÷ 0.75 = 72. A quarter of 72 is 18, and 72 − 18 = 54.
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