Is that really true?
Is 50% off and then another 20% off really 70% off?
The Simple Answer
No. A 50% discount followed by another 20% discount takes 60% off the original price, not 70%.
The second discount is taken off a price that is already lower, so it removes less money than you might expect. Here is a jacket that starts at $100.
A $100 jacket, 50% off and then 20% off
Take 50% off: $100.00 - $50.00 = $50.00
Take 20% off that: $50.00 - $10.00 = $40.00
You pay $40.00, so you saved $60.00 on a $100.00 jacket. That is 60%, not 70%.
Why the second discount is smaller
Twenty percent of $100 is $20. But by the time the 20% comes off, the jacket costs $50, and twenty percent of $50 is only $10. Each discount works on whatever price is left, so a second discount always bites into a smaller number than the first one did.
A shortcut: multiply what is left
Every discount leaves a share of the price behind. Fifty percent off leaves 50%, which is 0.50. Twenty percent off leaves 80%, which is 0.80. Multiply the two: 0.50 × 0.80 = 0.40. You pay 40% of the original price, so the total discount is 60%.
| First, then second | You pay | Total discount |
|---|---|---|
| 10% then 10% | 81% of the price | 19% |
| 20% then 20% | 64% of the price | 36% |
| 30% then 20% | 56% of the price | 44% |
| 40% then 25% | 45% of the price | 55% |
| 50% then 20% | 40% of the price | 60% |
| 50% then 50% | 25% of the price | 75% |
Does the order matter?
No. Multiplication gives the same answer in either order. Take 20% off the $100 jacket first and it costs $80; take 50% off that and you pay $40. The same $40 either way.
What about a coupon at the till?
Read the wording. A coupon for a percentage usually takes that percentage off the price you are about to pay, which is the stacking above. A coupon for a dollar amount takes the same money off whatever the price is. Shops differ in how they apply them, so look at the final price on the screen before you pay.
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