Discount

Three prices run through every discount sum: the cost price the shopkeeper paid, the marked price printed on the label, and the selling price actually charged. Discount is taken on the marked price; profit is taken on the cost price. Keep those two bases apart and the topic is easy.

SP = MP × (100 − d)/100 and discount % = (MP − SP)/MP × 100

The four types:

1. One discount. Apply the formula directly.
2. Successive discounts. Apply them one after the other, never by adding: 20% then 10% leaves 0.8 × 0.9 = 0.72 of the marked price, so the single equivalent discount is 28%, not 30%. For two discounts the shortcut is a + b − ab/100.
3. Discount together with profit. The chain is cost price → marked price → selling price. A shopkeeper who marks goods 40% above cost and then allows 25% discount sells at 1.40 × 0.75 = 1.05 times cost, a profit of 5%.
4. Offers in disguise. "Buy 3 get 1 free" means four articles for the price of three, a discount of 1/4 = 25%.

The single most common mistake is adding successive discounts. Two discounts of 10% are not 20%: the second is taken on a smaller amount, so the total is 19%. How to spot it: a correct answer for successive discounts is always less than the sum of the two figures.

The second most common is mixing the bases — reading "25% discount" as 25% profit or loss. Ask each time: percentage of which price?

SP = MP × (100 − d)/100 · discount % = (MP − SP)/MP × 100 · successive discounts multiply: 20% then 10% → 0.8 × 0.9 = 0.72, i.e. 28% · shortcut a + b − ab/100 · discount is on MP, profit is on CP · buy 3 get 1 free = 25%

The marked price of a cycle is ₹1,200 and the shop allows successive discounts of 20% and 10%. Find the selling price. → After the first discount: 1200 × 80/100 = ₹960. After the second, taken on ₹960: 960 × 90/100 = ₹864. Sanity check: the single equivalent discount is 100 − 72 = 28%, and 28% of ₹1,200 is ₹336, leaving 1200 − 336 = ₹864 — the same answer. Note that adding the discounts would have given 30% and a wrong price of ₹840.