Successive Discounts: Why 20% Off Plus 10% Is 28%

Two discounts in a row do not add up. A shop that takes 20% off and then another 10% off is not giving 30% off, but 28% off. This guide explains why, gives the formula, works through examples with prices, and shows how to spot the real saving behind offers that stack.

Why 20% plus 10% is 28%

The second discount is worked out on the price after the first one, not on the original price. Take an item marked ₹1,000. The first discount of 20% takes off ₹200 and leaves ₹800. The second discount of 10% is 10% of ₹800, which is ₹80, not ₹100. The price you pay is ₹720, so you saved ₹280, which is 28% of the original ₹1,000.

The formula

PrepShots gives the final price for two discounts of a% and b% as the marked price × (100 − a) ÷ 100 × (100 − b) ÷ 100. ExamAtlas gives the single equivalent discount as a + b − (a × b) ÷ 100. For 20% and 10% that is 20 + 10 − (200 ÷ 100) = 28%. Both forms give the same answer. The calculator uses the multiplication form:

Price you pay = original price × (1 − a/100) × (1 − b/100)

The effective discount is then the amount saved divided by the original price.

The order does not matter

Both pages say the order of the discounts does not change the final price, and the reason is that multiplication works in either order. Taking 20% off and then 10% off gives ₹720 on ₹1,000. Taking 10% off and then 20% off gives the same ₹720. This is useful when a shop applies a member discount and a sale discount in different orders on different days.

More worked examples

• ₹2,500 with 20% and then 10% off: ₹2,500 × 0.8 × 0.9 = ₹1,800. You save ₹700, which is 28%.
• ₹2,000 with 25% and then 20% off: ₹2,000 × 0.75 × 0.80 = ₹1,200. The effective discount is 40%, not 45%.
• ₹5,000 with 40% and then 10% off: ₹5,000 × 0.6 × 0.9 = ₹2,700. You save ₹2,300, which is 46%.
• 50% off and then another 50% off: the price falls to 25% of the original, so the effective discount is 75%, not 100%.

Equal discounts and "buy more, get more free"

ExamAtlas includes an example where two equal discounts take ₹1,000 to ₹810. Since 810 ÷ 1,000 = 0.81 and 0.81 is 0.9 × 0.9, each discount is 10%. The same page points out that a deal like buy 3, get 1 free is worth 25% off, because you pay for three of the four items.

That last idea is handy in shops. To compare offers, turn each one into an effective percentage, and then you can see which one is really cheaper.

Working backwards

If you know the sale price and the discounts, divide the sale price by the product of the factors to find the original price. If you paid ₹720 after 20% and 10% off, divide by 0.8 × 0.9 = 0.72 to get ₹1,000. This is a useful check when a price tag has been changed or a coupon is stacked on a sale.

A second check: if a tag says ₹1,800 after 20% and 10% off, the original price was ₹1,800 ÷ 0.72 = ₹2,500. And if you only know the total saving, say 28%, you can find the price paid by multiplying the original by 0.72. Doing this a few times makes it easy to judge any stacked offer in your head.

Common mistakes

• Adding the percentages. 20% and 10% is 28%, never 30%.
• Applying the second discount to the original price instead of the reduced price.
• Forgetting that a discount before tax and a discount after tax can differ if the tax is added at the end. Check which price the discount applies to.

How to use the calculator

Enter the original price and the first discount. If a second discount applies, enter it too and the calculator shows the price after each step, the amount you save and the effective discount. Leave the second box empty for a single discount.

Sources

• Successive Discount: Formula, Tricks and Examples (PrepShots)
• Successive Discount Formula and Examples (ExamAtlas)