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Business Mathematics and Statistics · Ch 1 — Profit and Loss

Marked Price and Discount

3

Marked Price and Discount

In retail trade, a shopkeeper usually fixes a price higher than the intended selling price and displays it on the article or on a price tag. This displayed price is the marked price (MP), also called the list price or catalogue price. To attract customers or clear stock, the shopkeeper then offers a discount — a reduction on the marked price.

Discount is always reckoned on the marked price (never on the cost price and never on the selling price):

Discount=MP−SP,Discount%=DiscountMP×100.\text{Discount} = MP - SP, \qquad \text{Discount}\% = \frac{\text{Discount}}{MP}\times 100.

Hence the selling price after a single discount of d%d\% is

SP=MP−Discount=MP(1−d100).SP = MP - \text{Discount} = MP\left(1 - \frac{d}{100}\right).

Important

Three prices, three different bases

Keep the reference of each percentage straight:

  • Profit% / Loss% are measured on the cost price.
  • Discount% is measured on the marked price.

A single problem may involve all three prices at once — e.g. an article is marked above its cost price, then sold at a discount, and the question asks for the final profit or loss. Work through the chain CP→MP→SPCP \to MP \to SP in order, applying each percentage to its own correct base. …

Definition 1Marked Price (MP)

The price printed on an article or its tag, before any discount; also called the list price or …

Definition 2Discount

A reduction offered on the marked price. Discount=MP−SP\text{Discount} = MP - SP, and Discount%=MP−SPMP×100\text{Discount}\% = \dfrac{MP-SP}{MP}\times 100 — always meas …

Definition 3Selling Price after Discount

SP=MP(1−d100)SP = MP\left(1 - \dfrac{d}{100}\right), where d%d\% is the rate of discount on th …