Marked Price and Successive Discounts: Follow the Changing Base

Three prices, three different jobs

A shirt has a price tag of ₹1,000. This is its marked price (MP). A 20% discount reduces the amount the customer pays. The discount is based on the marked price: (20/100) × 1,000 = ₹200. Therefore the selling price (SP) is 1,000 − 200 = ₹800. This alone does not tell us the seller's profit: we still need the cost price.

If the shirt cost the seller ₹640, profit = 800 − 640 = ₹160. Profit percentage uses CP: 160/640 × 100 = 25%. A 20% discount can therefore coexist with a 25% profit; the percentages compare different amounts.

Two discounts happen one after another

An item marked ₹1,000 receives 20% off, then an additional 10% off the reduced price. Ignore taxes and other charges.

1. First discount = 20% of 1,000 = ₹200. Remaining price = ₹800.
2. The second discount is 10% of ₹800, not ₹1,000: ₹80.
3. Final price = 800 − 80 = ₹720.
4. Total reduction = 1,000 − 720 = ₹280.
5. Equivalent discount = 280/1,000 × 100 = 28%, not 30%.

Why can we write 1,000 × 0.80 × 0.90? After removing 20%, 80% remains. After removing a further 10%, 90% of that remaining price stays. The multipliers describe those two operations; they are not unexplained shortcuts.

Find an unknown marked price

A book sells for ₹360 after a 10% discount. Let its marked price be x. The customer pays 90% of x, so 0.90x = 360. Divide both sides by 0.90: x = ₹400. Check: 10% of 400 is 40; 400 − 40 = 360.

A common mistake

Adding 20 + 10 assumes both discounts apply to the same original price. Here the second base is smaller. Read whether the question says successive discounts or two reductions calculated separately on the marked price; those are different conditions.

Check yourself

1. MP ₹1,500; discount 12%. Find SP.
2. MP ₹2,000; successive discounts 10% and 10%. Find final price and equivalent discount.
3. SP ₹850 after 15% discount. Find MP.

Answers: (1) discount 180, SP ₹1,320. (2) 2,000 → 1,800 → ₹1,620; reduction 380/2,000 × 100 = 19%. (3) 0.85x = 850, so MP ₹1,000.

Original practice examples; no previous-year attribution.