Profit and loss questions appear in almost every government exam paper. They look wordy, but they all use the same few ideas: cost price, selling price, marked price and percentage. Learn the formulas below and practise the tricks, and these questions become quick marks. If your percentage basics are weak, read our percentage formulas page first.

Key terms

  • Cost price (CP): the price at which an item is bought.
  • Selling price (SP): the price at which it is sold.
  • Marked price (MP): the listed price, from which a discount is given.
  • Profit: SP − CP, when SP is more than CP. Loss: CP − SP, when CP is more than SP.

Core formulas

  • Profit % = (Profit / CP) × 100 and Loss % = (Loss / CP) × 100. The base is always the cost price.
  • SP = CP × (100 + Profit %) / 100 when there is a profit.
  • SP = CP × (100 − Loss %) / 100 when there is a loss.
  • CP = SP × 100 / (100 + Profit %) or SP × 100 / (100 − Loss %).

Example 1. An item bought for ₹800 is sold for ₹920. Profit = 120, so profit % = 120/800 × 100 = 15%.

Example 2. An item sold for ₹1,440 earns a 20% profit. CP = 1,440 × 100/120 = ₹1,200.

Example 3. A trader sells an item for ₹900 at a 10% loss. CP = 900 × 100/90 = ₹1,000.

Discount

Discount is given on the marked price. Discount = MP − SP, and Discount % = (Discount / MP) × 100. Also, SP = MP × (100 − Discount %) / 100.

Example 4. The marked price is ₹1,200 with a 15% discount, so SP = 1,200 × 0.85 = ₹1,020. If this gives a 2% profit, CP = 1,020 / 1.02 = ₹1,000.

Successive discounts

For two successive discounts of a% and b%, the single equivalent discount is a + b − (a × b)/100.

Example 5. Discounts of 20% and 10% are equal to 20 + 10 − 2 = 28%. Check: 100 → 80 → 72, which is a 28% reduction.

Markup and discount together

If an item is marked m% above cost and then sold at a d% discount, the net profit percentage is m − d − (m × d)/100.

Example 6. A shopkeeper marks goods 40% above cost and gives a 25% discount. Net profit = 40 − 25 − 10 = 5%. Check: 100 → 140 → 105.

Two articles at the same selling price

If two articles are sold at the same price, one at a p% profit and the other at a p% loss, there is always a loss of p²/100 % overall.

Example 7. Two items are sold at the same price, one at 10% profit and one at 10% loss. The net loss is 10²/100 = 1%.

Cost price equals selling price of different quantities

Suppose the cost of 12 articles equals the selling price of 10 articles. The profit percentage = (12 − 10)/10 × 100 = 20%. The rule: profit % = (articles bought − articles sold)/articles sold × 100.

False weights

A dishonest shopkeeper who sells 900 g while claiming 1 kg has an error of 100 g. His profit % = error/(true weight − error) × 100 = 100/900 × 100 = 11.11%.

Handy ratio trick

With a profit of 25%, the ratio CP : SP is 100 : 125 = 4 : 5. With a loss of 20%, CP : SP is 100 : 80 = 5 : 4. Thinking in ratios usually beats long formulas when you are short of time.

Common mistakes to avoid

  • Calculating profit or loss percent on the selling price. It is always on the cost price, unless the question says otherwise.
  • Calculating discount on the cost price. Discount is always on the marked price.
  • Adding successive discounts directly. Two discounts of 10% are 19%, not 20%.
  • Ignoring the overall loss when two items are sold at the same price.

Practice questions

  1. An item costs ₹250 and sells for ₹300. What is the profit percentage?
  2. The marked price is ₹500 and the discount is 20%. What is the selling price?
  3. An item is sold for ₹1,140 at a 5% loss. What is the cost price?
  4. What single discount equals two successive discounts of 10% each?
  5. Goods are marked 50% above cost and sold at a 20% discount. What is the profit percentage?

Answers: 1) 20%, 2) ₹400, 3) ₹1,200, 4) 19%, 5) 20%.

How to practise

Solve ten profit and loss questions a day for a week and write the formula next to each one you miss. Then try them in our mock tests, and check where this topic fits in the SSC CGL syllabus.

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