30% off then a further 20% off is 44% off. Not 50%.
The second discount applies to the already-reduced price, so it takes 20% of a smaller number than you might expect.
Working it out
Stop thinking about what comes off and start thinking about what is left.
- 30% off leaves 70% of the price → ×0.7
- 20% off leaves 80% of what remains → ×0.8
0.7 × 0.8 = 0.56You pay 56% of the original, so you saved 44%.
On a 100 item: 30% off takes it to 70, then 20% off takes 14 more off, landing at 56. The second discount was worth only 14, not the 20 it appeared to promise.
The order makes no difference
A common suspicion is that stores apply the discounts in whichever order suits them. They cannot — multiplication does not care about order.
0.7 × 0.8 = 0.56
0.8 × 0.7 = 0.56Identical. If a store tells you the order matters for the discount itself, something else is going on — usually a coupon that excludes already-reduced items.
The gap grows with the numbers
| Stacked | Actually | Sounds like |
|---|---|---|
| 10% + 10% | 19% | 20% |
| 20% + 20% | 36% | 40% |
| 30% + 20% | 44% | 50% |
| 50% + 50% | 75% | 100% |
| 50% + 20% + 10% | 64% | 80% |
That fourth row is the important one. 50% + 50% is not free. It is 75% off, and stacking never reaches 100% no matter how many discounts you add, because you are always taking a fraction of something that still exists.
Why the advertising works
“30% off, plus an extra 20% off everything” reads as half price to almost everyone. It is 44%, which is a genuinely good discount — but the perceived saving is meaningfully larger than the real one, and that difference is doing real work in the marketing.
The same structure appears as “buy one get one 50% off”. Two items at full price and half price is 25% off the pair, not 50%.
Doing it quickly
Convert each discount to what remains, multiply, then subtract from 1.
For 25% and 15%: remaining is 0.75 and 0.85, which multiply to about 0.64, so roughly 36% off.
A rough shortcut for small discounts: add them, then subtract a bit. Two discounts of a and b percent come to about a + b − (a × b ÷ 100). For 30 and 20 that is 50 − 6 = 44%, which is exact here and close enough elsewhere.