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Discount and Marked Price: Explained with Examples

MathematicsTry the interactive 3D model →

The marked price (MP) is the price printed on the tag, and a discount is the reduction the shop offers on it. If a shirt is marked Rs. 1,200 and the shop offers 15% off, you pay Rs. 1,020. The discount exists to attract buyers while still leaving the seller a profit over the cost price.

This matters because almost nothing sells at its marked price today — clothes, electronics, furniture and even medicines carry discounts. Knowing how marked price, discount and selling price connect lets you verify sale claims, compare offers from two shops, and spot when a huge discount was created by inflating the marked price first.

Key Concepts

  • Marked price (MP): the labelled price before any discount. Also called list price.
  • Discount: the amount subtracted from MP, usually quoted as a percentage of MP.
  • Selling price (SP): what you actually pay: SP = MP − Discount.
  • Successive discounts: two discounts applied one after another, for example 20% then 10%, which is not the same as 30% off.
  • Cost price link: the seller's real profit is still measured against CP, not MP.

Formulas

  • Discount = MP − SP; Discount% = (Discount ÷ MP) x 100 (always on MP).
  • SP = MP x (1 − discount%/100).
  • MP = SP x 100/(100 − discount%).
  • Successive discounts d1% then d2%: effective discount = (d1 + d2 − d1 x d2/100)%.

Worked Example

A jacket is marked Rs. 1,200 with a 15% discount. Find the selling price.

  1. Discount = 15% of MP = (15/100) x 1200 = Rs. 180.
  2. SP = MP − Discount = 1200 − 180 = Rs. 1,020.
  3. Shortcut check: SP = 1200 x (1 − 15/100) = 1200 x 0.85 = Rs. 1,020. Correct.

Common Misconceptions

  • “20% off followed by 10% off is 30% off.” Wrong. On Rs. 1,000: after 20%, Rs. 800; 10% off Rs. 800 is Rs. 80, so you pay Rs. 720 — an effective 28% discount, not 30%.
  • “Discount% is calculated on the selling price.” Wrong. Like profit%, it has a fixed base: discount% is always on the marked price.
  • “A bigger discount always means a better deal.” Wrong. 50% off an inflated MP of Rs. 2,000 (pay Rs. 1,000) loses to another shop selling the same item flat for Rs. 900.

Real-World Applications

  • Retail sales: end-of-season sales, festival offers and coupon codes all run on these formulas.
  • Online shopping: comparing “40% off” across sites requires converting each to the actual SP.
  • Business: sellers set MP high enough that the discounted SP still covers CP plus target profit.

Discount always comes off the marked price, and the selling price is MP shrunk by that percent. Watch out for successive discounts — they multiply, they don't add. With these formulas you can price-check any sale tag in seconds.

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