Reverse Percentages: Work Backwards Without Guessing
Find an original price or value before a percentage increase or decrease using reverse multipliers and simple checks.
What “reverse percentage” means
You know the final value after a percentage change, but you need the original. For example, a jacket costs ₹1,680 after a 20% discount. The ₹1,680 represents 80% of the original price, not 100%.
The reliable method
- Turn the final percentage into a multiplier.
- Write
original × multiplier = final. - Divide the final value by the multiplier.
Original price: ₹2,100.
Reverse an increase
If a salary becomes ₹54,600 after a 5% increase, the final value is 105% of the original.
Original salary: ₹52,000.
Why subtracting the percentage is wrong
A common wrong move is to take 20% of the discounted price and add it back. But the 20% discount was calculated from the original, which is a different base. Reverse percentage questions are about undoing a multiplication, so division is the natural inverse operation.
Quick check
Memory trick
Forward percentage change = multiply. Reverse percentage change = divide by the same multiplier.
A phone costs 2,700 after a 10% discount. What was the original price?
Keep going
For another problem using related ideas, return to the Fractions, Ratios & Percentages page.