Sale and coupon discount price:
why 20% plus 10% is not 30%

One discount is simple; two are not

A single percentage discount is direct: the sale price is the original price times one minus the percentage. A 25% reduction on ₹4,000 is 4,000 × 0.75 = ₹3,000.

The trouble starts when two reductions meet, such as a festival sale plus a coupon code, or 'extra 10% off already discounted items'. People add the percentages in their heads, and that overstates the saving.

The second discount applies to the price left after the first, not to the original. It therefore takes a smaller bite, and the sum of the two is always a little less than the headline total.

Multiplying factors, then a flat coupon

The order of two percentage discounts does not matter. 10% then 20% gives 4,000 × 0.90 × 0.80 = ₹2,880 as well, because multiplication is commutative.

A coupon for a fixed amount, such as ₹300 off, behaves differently, because subtracting before or after a percentage changes how much the percentage bites.

In general, take percentage discounts off the price first, then the flat amount, if you have a choice. Often the shop dictates the order: many apps apply coupons to the pre-discount price or to the cart total, so read the final screen before paying.

Working backwards from a sale price

To find the original price from the sale price and one or more percentage discounts, divide by the product of the factors.

To compute the effective discount from two prices, use (original − paid) ÷ original. That is how to compare two offers whose headline figures are different.

Why a discount and a markup do not cancel

A percentage off and the same percentage back on do not return you to the start, because each applies to a different base. A 20% reduction leaves 80% of the price; to get back to 100% you need a rise of 25%, since 0.80 × 1.25 = 1.

The same asymmetry shows up in shops that 'mark down' and 'mark up' in cycles. It is also the reason that a 50% fall in price needs a 100% rise to recover.

Reading sale claims with a sceptical eye

The best defence is to compare the final price on the checkout page with the price on a few other sellers, or in the product's price history where it is available. A discount from an inflated reference price is not a bargain.

Percentage is not price

A larger percentage on a higher list price does not always give the lower final price. Compare what you pay.

The same applies to cashback. ₹200 cashback on a ₹2,000 order is a 10% return, but it arrives later, often as wallet credit that must be spent on that platform, so it is worth somewhat less than a 10% price cut at the till.

When two offers are close, write the final amount, any cashback and any delivery or handling fees on one line each, then compare the net. The percentage in the banner never settles it.

Three or more layers and limits

The factor method extends: multiply as many (1 − d) terms as there are discounts. A 20% sale, a further 10% member discount and 5% card offer give 0.80 × 0.90 × 0.95 = 0.684, so a 31.6% total reduction instead of the 35% that adding suggests.

• Maximum caps: many coupons cap the saving at a rupee amount, so a 10% coupon on a ₹20,000 order may stop at ₹500.
• Minimum order: a threshold may disqualify the coupon if an item is removed.
• Exclusions: sale items are often excluded from coupons, or the other way round.
• Taxes: confirm whether the discount is applied before or after tax, since it changes the final amount slightly.

A calculator for each of these offers lets you enter the price and see the final amount at once, but the ideas above explain why the results come out as they do.

A full checkout walked through

Put the pieces together with one realistic basket. A jacket is listed at ₹5,000. The festival sale takes 30% off. A member offer gives a further 10% off the sale price. A coupon takes ₹250 off the cart. Delivery is ₹60.

Add the headline numbers and you would expect 30% + 10% = 40% plus ₹250, which comes to ₹2,750 before delivery. The true price is ₹150 higher, because the member discount worked on the reduced price. This is not a trick; it is how percentages behave, and the checkout page is the final authority.

Before paying, check three things: whether delivery or a handling charge cancels part of the saving, whether the return policy applies to sale items, and whether the same item is available at a lower final price elsewhere. A discount is only a saving if you would have bought the product at the full price, or if the final price is lower than any realistic alternative.