“30% off plus an extra 10%” is not 40% off
This is the single most profitable piece of arithmetic in retail. Two discounts applied one after another multiply — they do not add — because the second one is taken from a price that has already shrunk.
A $89 jacket at 30% off, then a further 10% at checkout
- After the first 30%
- 89 × 0.70 = $62.30
- After the further 10%
- 62.30 × 0.90 = $56.07
- Total saved
- $32.93
Effective discount: 37%, not 40%
The three-point gap sounds trivial, but it is the entire reason the offer is structured that way. “30% plus 10%” reads as a bigger number than “37% off” while costing the retailer less. Here is how common stacked pairs really land:
| Advertised | Sounds like | Actually |
|---|---|---|
| 20% + 10% | 30% off | 28% off |
| 30% + 10% | 40% off | 37% off |
| 40% + 20% | 60% off | 52% off |
| 50% + 25% | 75% off | 62.5% off |
The bigger the discounts, the wider the gap. At the extreme, stacking can never reach 100% — each cut only ever removes a fraction of what is left.
Recovering the original price
Working backwards catches inflated “was” prices. If something is $62.30 after 30% off, do not add 30% back — that gives $80.99 and is wrong, because the discount was calculated from the original, not the sale price. Instead divide by what remains: 62.30 ÷ 0.70 = $89. If the tag claims the original was $120, the maths says otherwise.
Does the order of the discounts matter?
No. Multiplication is commutative, so 30% then 10% gives exactly the same final price as 10% then 30% — both are 0.63 of the original. If a cashier applies your coupons in a different order than you expected, the total is unaffected. The one exception is when a store caps a coupon at a maximum value, in which case applying it to the larger amount first can matter.