Why is 20 percent off plus another 10 percent off not 30 percent?

A customer sees a board saying "20 percent off" and, at billing, a coupon takes another 10 percent. Many people assume they got 30 percent off. They did not, and the difference matters if you are the one running the sale.

The reason

The second discount is calculated on the already reduced price, not on the original. So the two discounts are applied one after the other, and they multiply instead of adding.

A worked example

Start with an item priced at Rs 100.

• 20 percent off takes Rs 20, leaving Rs 80
• 10 percent off Rs 80 takes Rs 8, leaving Rs 72

The final price is Rs 72. The total discount is Rs 28 on a Rs 100 item, which is 28 percent, not 30.

You can see it as multiplication. A 20 percent discount means paying 0.8 of the price. Another 10 percent means paying 0.9 of that. 0.8 x 0.9 = 0.72. So the customer pays 72 percent of the original.

Reversing the order gives the same answer. Take 10 percent first, leaving Rs 90, and then 20 percent off that, leaving Rs 72. The order does not change the result.

What it means for your profit

Say the item costs you Rs 50 in all.

• A true 30 percent off gives a price of Rs 70, and profit is Rs 20
• Stacked 20 plus 10 percent gives a price of Rs 72, and profit is Rs 22

So stacking costs you Rs 2 less per unit than a flat 30 percent would. On Rs 100 items, that does not look like much. On a Rs 1,000 item, the price would be Rs 720 against Rs 700, a Rs 20 gap per sale. Over 200 sales that is Rs 4,000.

This works in your favour, but here lies the trap. Your customer may feel cheated if she expected 30 percent, and your staff might promise "30 percent off" on a call when the system gives 28. Be clear on your wording.

Where stacking happens in a small store

• A product already marked down, then a coupon code on top
• A festival sale plus a first-order coupon
• A bundle discount plus a payment-mode discount

Decide in advance whether codes may be combined. Many sellers get surprised only when they see the invoices. The safest approach is to allow one offer at a time, or to test the worst combination on a sample product and check the profit that remains.

Check before you launch

Work out the final price when every offer you run is applied together. If you have a 25 percent sale and a 15 percent first-order code, the combined price is 0.75 x 0.85 = 0.6375, so the customer pays about 63.75 percent, a discount of about 36.25 percent. Is your profit still positive at that price? Many sellers find that it is not.

A habit worth keeping

Whenever you compare discounts, convert them to the price the customer pays, not the percentage off. It is easier to see that Rs 72 against Rs 70 is a small gap than to reason with percentages. If you need to go back from a discounted price to the original, see how to find the original price from a discounted price. And for what a single cut does to your margin, read how a 10 percent discount hits profit.