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Aptitude · 3 min lesson · 10 questions

Profit and Loss

Profit and loss questions test whether you can keep track of a few simple terms and apply one percentage rule consistently. They are common in campus placement papers because they combine percentages with everyday situations such as shops, discounts and sales. Once you know the terms, most questions reduce to two formulas.

The terms

  • Cost price (CP): the price at which an item is bought, including any extra costs such as transport or repairs.
  • Selling price (SP): the price at which it is sold.
  • Profit: SP − CP, when SP is greater.
  • Loss: CP − SP, when CP is greater.
  • Marked price (MP): the price written on the item, before any discount.
  • Discount: the reduction from the marked price. SP = MP − discount.

The golden rule

Profit % and loss % are always calculated on the cost price, unless the question says otherwise. Discount % is always calculated on the marked price.

Profit % = (Profit / CP) × 100, and Loss % = (Loss / CP) × 100.

The two formulas that solve most questions

  1. SP = CP × (100 + P) / 100 for a profit of P%, or CP × (100 − L) / 100 for a loss of L%.
  2. CP = SP × 100 / (100 + P) for a profit of P%, or SP × 100 / (100 − L) for a loss of L%.

Think of it as multipliers: a 20% profit means SP = 1.2 × CP, a 15% loss means SP = 0.85 × CP, and a 10% discount means SP = 0.9 × MP.

Discount questions

A shopkeeper usually marks an item above its cost and then gives a discount. Chain the multipliers: if the marked price is 25% above cost and the discount is 20%, then SP = CP × 1.25 × 0.80 = CP × 1.00. There is no profit and no loss.

For two successive discounts of a% and b%, the single equivalent discount is a + b − (a × b)/100. Two discounts of 20% and 10% equal 20 + 10 − 2 = 28%, not 30%.

Equal selling price, equal percentage

If two items are sold at the same price, one at a profit of x% and the other at a loss of x%, there is always an overall loss of x²/100 % on the total cost. With 10% it is 1%. The reason is that the profit is taken on a smaller cost and the loss on a larger one.

Worked examples

Example 1. An article costing 640 is sold for 736. Profit = 96, so profit % = 96 / 640 × 100 = 15%.

Example 2. A trader sells an article at a 20% loss and gets 600. The CP is 600 × 100 / 80 = 750.

Example 3. The marked price of a bag is 2,000, and a 25% discount is given. SP = 2,000 × 0.75 = 1,500. If the CP was 1,200, the profit is 300, which is 300 / 1,200 × 100 = 25%.

Example 4. A dealer marks goods 25% above cost, then gives a 20% discount. SP = CP × 1.25 × 0.8 = CP. So there is no profit and no loss.

Common mistakes

  • Calculating profit % on the selling price instead of the cost price.
  • Forgetting to add extra costs (repairs, transport) to the cost price.
  • Treating a "10% profit then 10% loss" as zero overall. Use the multipliers: 1.1 × 0.9 = 0.99, a loss of 1%.
  • Applying a discount to the cost price instead of the marked price.

Exam tips

  1. Assume CP = 100 when only percentages are given. It keeps the numbers small.
  2. Write the multiplier chain on paper before calculating.
  3. Check that your answer is sensible: a profit with a lower SP than CP means an error.

When you are ready, try the quiz. The explanation after each question shows the multiplier method so you can compare it with yours.

Practice quiz: Profit and Loss

Pick an answer for each question. You will see the correct answer and the reason straight away. Your best score is saved on this device only.

  1. An article bought for 500 is sold for 575. What is the profit percentage?

  2. A trader buys an item for 800 and sells it at a 12% loss. What is the selling price?

  3. A shopkeeper earns a 25% profit by selling an article for 750. What was the cost price?

  4. The marked price of a jacket is 1,200 and a 15% discount is offered. What is the selling price?

  5. A shopkeeper marks goods 40% above cost and allows a 10% discount. What is his profit percentage?

  6. A man sells two articles at 990 each. On one he gains 10% and on the other he loses 10%. What is his overall loss (in rupees)?

  7. The selling price of 15 items equals the cost price of 20 items. What is the profit percentage?

  8. Two successive discounts of 20% and 10% are equal to a single discount of what percent?

  9. A man buys an article for 250, spends 50 on repairs and sells it for 360. What is his profit percentage?

  10. By what percent above cost price must an item be marked so that a 10% discount still leaves a 20% profit?

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