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Commercial mathematics

Profit, loss & discount: follow the price

Separate cost price, marked price and selling price, then calculate percentage changes using the correct base.

IntermediateAbout 14 min3 worked examples
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01 / THE STARTING POINT

Before you begin

What you need: Percentages and decimal multipliers.

  • Distinguish cost, marked and selling prices
  • Find profit or loss percentages
  • Combine discounts and reverse price changes
02 / BUILD THE CONCEPT

Understand the idea

Three prices, three jobs

Cost price (CP) is the amount paid to acquire an item. Marked price (MP) is the advertised price. Selling price (SP) is the final amount received after discounts.

Profit and loss compare with cost

Profit = SP − CP when SP is larger. Loss = CP − SP when CP is larger. Their percentages use CP as the denominator because cost is the starting investment.

Discount compares with marked price

Discount = MP − SP and discount percentage uses MP as its base. An item can be discounted and still sold at a profit if its marked price was sufficiently above cost.

03 / A DIFFERENT WAY TO SEE IT

A discount can still leave a profit

  1. Cost ₹800
  2. Marked ₹1,200
  3. 20% off → ₹960
  4. Profit ₹160
Discount is ₹240 on the marked price. Profit is ₹160 on the cost, giving a 20% profit.
04 / FROM IDEA TO ANSWER

A method you can reuse

KEEP THIS HANDY

Profit % = (SP − CP)/CP × 100%

For a profit and positive CP. For a loss use (CP − SP)/CP. SP after d% discount = MP × (1 − d/100).
  1. Label each given amount CP, MP or SP.
  2. Choose the correct base: CP for profit/loss; MP for discount.
  3. Use multipliers for successive changes and verify the final price.
A useful insight

For successive discounts a% and b%, the equivalent discount is (a + b − ab/100)%. This follows by multiplying the remaining-price factors.

05 / WATCH THE METHOD WORK

Worked examples

Read the question first. Try a step yourself, then compare your reasoning.

EXAMPLE 01

Profit percentage

An item costs ₹800 and sells for ₹920. Find profit percent.

  1. Profit = ₹920 − ₹800 = ₹120.
  2. Use cost ₹800 as the base.
  3. 120/800 × 100% = 15%.
Answer15% profit
EXAMPLE 02

Successive discounts

A ₹2,000 item has discounts of 10% and then 20%. Find the final price.

  1. After the first discount: 2000 × 0.9 = 1800.
  2. After the second: 1800 × 0.8 = 1440.
  3. The overall discount is 560/2000 = 28%.
Answer₹1,440
EXAMPLE 03

Recover cost

An item sells for ₹540 at a 10% loss. Find its cost.

  1. SP is 90% of CP.
  2. 0.9 × CP = 540.
  3. CP = 540 ÷ 0.9.
Answer₹600
06 / YOUR TURN

Check your understanding

Quick questions, with explanations. These are for self-study and do not affect your account score.

0 of 3 questions checked

QUESTION 1CP is ₹500 and SP is ₹600. Profit percent?

See the explanation

20%. Profit is ₹100. Divide by CP ₹500 to get 20%.

QUESTION 2A marked price of ₹1,500 is discounted 20%. Find SP.

See the explanation

₹1,200. 1500 × 0.8 = 1200.

QUESTION 3Two 10% discounts give what total discount?

See the explanation

19%. The remaining multiplier is 0.9 × 0.9 = 0.81, so the discount is 19%.

07 / TAKE THE NEXT STEP

Put your understanding to work

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EXPLORE THE NUMBERS

Profit or Loss Calculator

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Profit Loss and Discount Practice Quiz 1

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Profit Loss and Discount Practice Quiz 2

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Profit Loss and Discount Practice Quiz 3

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Profit and discount practice

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