Two successive 20% discounts amount to a total discount of 36%, not 40%. The second percentage applies to the price already reduced by the first discount, rather than to the original price. For a product priced at 100 currency units, the first reduction brings the price to 80; the second removes 16, leaving a final price of 64.
Why does the base change after each discount?
A percentage is always a fraction of a base amount. For the first discount, the base is 100. Once the price falls to 80, that is the amount used for the next calculation. Thus, 20% of the original price is 20, while 20% of the intermediate price is 16. The combined saving is 36, or 36% of the original 100.
| Step | Calculation base | Discount at this step | Price after this step |
|---|---|---|---|
| Original price | 100 | None | 100 |
| First 20% discount | 100 | 20 | 80 |
| Second 20% discount | 80 | 16 | 64 |
Adding 20% + 20% = 40% would be correct only if both reductions were calculated separately on the same original base and then subtracted. That is not a sequence of discounts.
How to calculate without subtracting at every step
A 20% discount leaves 80% of the amount, so it multiplies the price by 0.80. A second 20% discount means multiplying by 0.80 again:
Final price = original price × 0.80 × 0.80 = original price × 0.64.
The product retains 64% of its original price. The equivalent discount is therefore 100% − 64% = 36%. This multiplicative-factor approach follows the treatment of discounts and percentage changes in OpenStax mathematics materials.
Formula for two different discounts
For discounts of a% and b%, express each rate as a decimal and use final price = original price × (1 − a/100) × (1 − b/100). The equivalent total discount is [1 − (1 − a/100) × (1 − b/100)] × 100%. This formula assumes the second discount applies to the result of the first.
Example with 20% and 10% discounts
For an item originally priced at 200 currency units, a 20% discount reduces the price to 160. The next 10% discount is 16 because its base is 160. The final price is 144 and the saving is 56. Dividing 56 by the original 200 gives an equivalent discount of 28%, not 30%.
Using factors, 200 × 0.80 × 0.90 = 144. For two pure percentage discounts applied to the intermediate price, reversing their order does not change the mathematical result because multiplication is commutative. Do not automatically extend that rule to offers involving a fixed monetary reduction, discount caps, intermediate rounding, or specific coupon conditions.
How to check a successive-percentage calculation
- Write down the original price and the order of the offer's conditions.
- Convert each discount to the fraction retained: 20% becomes 0.80 and 10% becomes 0.90.
- Multiply the original price by the factors, updating the base at each step.
- Subtract the final price from the original price to find the monetary saving.
- Divide the saving by the original price and multiply by 100 to get the equivalent discount.
As a quick check, for two positive discounts below 100%, the equivalent percentage is less than the simple sum of the rates. If an offer says “20% + 20%,” check its terms: the 36% result assumes both reductions actually apply in sequence without additional restrictions.
