business · 2 min read · India
60% off then 40% off is not free
Successive discounts multiply rather than add. A 30% discount followed by a 20% discount leaves you paying 56% of the original price, an effective discount of 44% rather than 50%. The rule is to multiply what remains: 0.70 × 0.80 = 0.56. The order the discounts are applied in makes no difference to the final price.
A sign reading "60% off, then a further 40% off at the till" sounds like the whole price. Sixty and forty make a hundred, and a hundred percent off is free. It is not free. On a ₹1,000 item you pay ₹240, which is 76% off rather than 100%.
The reason is that the second discount is not taken from the price on the tag. It is taken from the price the first discount already left behind, and that is a smaller number, so the same percentage removes less money.
Follow what is left, not what is taken off
The arithmetic is easier in the other direction. Instead of tracking what comes off, track what stays on. A 30% discount leaves 70% of the price. A 20% discount leaves 80% of whatever it is applied to. Put them one after the other and you keep 70% of 80%, which is 0.70 × 0.80 = 0.56, so you pay 56% and the effective discount is 44%.
| Discounts | What you pay | Effective discount | The two added together |
|---|---|---|---|
| 30% then 20% | ₹560 | 44% | 50% |
| 10% then 10% then 10% | ₹729 | 27.1% | 30% |
| 60% then 40% | ₹240 | 76% | 100% |
| 50% once | ₹500 | 50% | 50% |
The gap widens as the discounts get larger, which is exactly when a shopper is paying most attention to the sign. At 10% and 10% the error is under three points. At 60% and 40% it is twenty-four, and it is the difference between paying nothing and paying a quarter.
The order does not matter
Thirty percent then twenty percent, or twenty percent then thirty percent, both leave ₹560 on a ₹1,000 item. Multiplication does not care about order, and neither does the till. This is worth knowing because it is the one thing people reliably expect to matter, and arguing about which discount should be applied first is arguing about nothing.
There is one case where order genuinely changes the answer, and it is not a percentage: a flat amount off, say ₹200, mixed in with a percentage. Taking ₹200 off first and then 30% off is not the same as 30% off first and then ₹200 off.
Reading it backwards
The same rule answers the question a shop asks rather than a shopper. If you want an advertised 50% off and you are already giving 30%, the second discount is not 20%. You need to keep 50% overall while already keeping 70%, so the second one must leave you with 0.50 ÷ 0.70, which is about 71.4%, making it a discount of roughly 28.6%.
- Two discounts: multiply what remains, so 30% and 20% give 0.70 × 0.80 = 0.56.
- The effective discount is one minus that, so 44% rather than 50%.
- Adding the percentages always overstates the discount, and never by a fixed amount.
- Order changes nothing while every discount is a percentage.
None of this is a trick being played on anyone. The sign is accurate, the till is accurate, and the arithmetic is the ordinary arithmetic of percentages applied one after another. It is only surprising because percentages read like quantities, and they are ratios.