Reverse Percentage

Find the original value before a percentage change was applied.

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Find the original value before a percentage change was applied.

Reverse percentage problems ask you to work backwards from a final value to find the original. If something increased by X%, the final value equals the original times (1 + X/100). To find the original, divide the final value by this multiplier. This is trickier than forward percentages because you can't simply subtract the percentage.

If Final = Original × (1 + X/100), then Original = Final ÷ (1 + X/100)

After a 20% increase, a price is $120. Original = $120 ÷ 1.20 = $100
After a 25% discount, a price is $60. Original = $60 ÷ 0.75 = $80
After a 10% raise, salary is $55,000. Original = $55,000 ÷ 1.10 = $50,000

How to recognize it

You're given the final value after a percentage change
You need to find what the value was before the change
Keywords: 'original price', 'was before', 'started at'

Common mistakes

Subtracting the percentage from the final (e.g., $120 - 20% = $96, wrong!)
Using the wrong multiplier (1.20 for increase, 0.80 for 20% decrease)
Confusing increase (multiply by >1) with decrease (multiply by <1)

Step-by-step walkthrough

After a 25% increase, a price is $150. What was the original price?

Identify the multiplier for a 25% increase: 1 + 25/100 = 1.25
Set up the equation: Original x 1.25 = $150
Divide the final value by the multiplier: $150 / 1.25
Calculate: $150 / 1.25 = $120

Answer: $120

Practice guidance

Numerical Reasoning