Reverse Percentage: Find the Original Value
After increase: original = final ÷ (1 + p/100). After decrease: original = final ÷ (1 − p/100)..
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Formula and worked example
After increase: original = final ÷ (1 + p/100). After decrease: original = final ÷ (1 − p/100).
$120 after a 20% increase came from $100. $80 after a 20% decrease came from $100. Adding the same percentage back is wrong because the base has changed.
Why reverse percentages use division
The percentage was applied to the unknown original value. Reversing the operation therefore means dividing the final value by the multiplier, not applying the percentage in the opposite direction.
Common mistake
Use the original value as the baseline for relative change. A percentage calculation can give a different answer when the denominator changes.
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Source & methodology
Reverse-percentage problems are solved by rearranging a percent proportion to recover the unknown base.