How to find the original price before a discount
Sometimes you see only the sale price and the discount, and you want to know what the item cost before. The tempting shortcut gives the wrong answer, and the correct method is only one step.
The tempting shortcut
A sweater costs $60 after 25% off. Many people take 25% of $60, which is $15, and add it back to get $75. That is not right, because the 25% was taken from the original price, not from $60.
The correct method
A discount leaves a share of the price behind. With 25% off, you pay the other 75%, which is 0.75 as a decimal. So the sale price is the original price times 0.75. To go backward, divide: original = sale price ÷ the share you pay.
A sweater at $60 after 25% off
Share you pay: 100% - 25% = 75%, or 0.75
Original price: $60 ÷ 0.75 = $80.00
Check: $80.00 × 0.75 = $60.00, and 25% of $80 is $20, so $80 - $20 = $60.
| Discount | Share you pay | Sale price $48 means original |
|---|---|---|
| 10% off | 0.90 | $53.33 |
| 20% off | 0.80 | $60.00 |
| 25% off | 0.75 | $64.00 |
| 40% off | 0.60 | $80.00 |
| 50% off | 0.50 | $96.00 |
Why the shortcut fails
Adding 25% to $60 gives $75, but $75 less 25% is only $56.25. The two percentages are taken from different starting prices, so they do not cancel. The bigger the discount, the bigger the error: at 50% off, the shortcut would turn a $48 sale price into $72 instead of $96.
A quick way to check
Take your answer and apply the discount again. If it lands on the sale price, you are right. For $80 at 25% off you get $60, which matches.
Discount Calculator: Enter the original price and the discount to see the sale price, then compare it with the price you were given.