Reverse a percentage change

Use the original value as 100% to work backwards from an increase or decrease.

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.

100% + 20% = 120%

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.

The original 80 plus an increase of 16 gives 96.

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%.

75% = 54. Find 100%.

Try it

What was the original price before the 25% discount?

  1. 67.50
  2. 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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