Profit and Loss: Formulas, Tricks and Solved Questions

Profit and Loss compares the cost price and selling price of an article. This topic includes profit, loss, profit or loss percentage, marked price, discount, and successive changes. The formulas help calculate unknown values such as cost price, selling price, gain, loss, discount, or the final price after multiple transactions.

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What is Profit and Loss?

Profit occurs when the selling price is greater than the cost price, while loss occurs when the selling price is less than the cost price. Profit and loss percentages are calculated on the cost price unless another base is explicitly stated.

Let CP be the cost price and SP be the selling price. Profit = SP − CP when SP > CP, and Loss = CP − SP when CP > SP. Profit percentage = (Profit ÷ CP) × 100 and Loss percentage = (Loss ÷ CP) × 100. For example, if CP = ₹500 and SP = ₹575, profit = ₹75 and profit percentage = (75 ÷ 500) × 100 = 15%.

Profit and Loss Formula & Tricks

Important Formulas

Profit
Profit = SP − CP

Use this when the selling price is greater than the cost price.

Loss
Loss = CP − SP

Use this when the cost price is greater than the selling price.

Profit Percentage
Profit% = (Profit ÷ CP) × 100

Profit percentage is calculated with cost price as the base.

Loss Percentage
Loss% = (Loss ÷ CP) × 100

Loss percentage is calculated with cost price as the base.

Selling Price from Profit
SP = CP × (100 + Profit%) ÷ 100

Use the numerical profit percentage in the formula.

Selling Price from Loss
SP = CP × (100 − Loss%) ÷ 100

Use the numerical loss percentage in the formula.

Discount
Discount = MP − SP

MP is the marked price and SP is the selling price.

Discount Percentage
Discount% = (Discount ÷ MP) × 100

Discount percentage is calculated on the marked price.

Quick Tricks

Use the ratio method for percentages

If an article is sold at a profit of p%, then CP : SP = 100 : (100 + p). If it is sold at a loss of l%, then CP : SP = 100 : (100 − l).

Example: At a 20% profit, CP : SP = 100 : 120 = 5 : 6. If SP is ₹720, CP = 720 × 5 ÷ 6 = ₹600.
Convert percentage changes into multipliers

A p% increase multiplies a value by (100 + p) ÷ 100, while a p% decrease multiplies it by (100 − p) ÷ 100.

Example: A 20% profit followed by a 10% loss gives a multiplier of 1.20 × 0.90 = 1.08, so the net result is an 8% profit.
Find gain or loss when CP and SP are reversed

If one article is sold at x% profit and another at x% loss for equal selling prices, the overall result is always a loss of x² ÷ 100 percent.

Example: At 20% profit and 20% loss with equal SP, overall loss = 20² ÷ 100 = 4%.
Handle false weights through actual quantity

If a seller gives w units while charging for 100 units, the gain percentage is ((100 − w) ÷ w) × 100, assuming the price per stated unit is unchanged.

Example: Giving 900 g while charging for 1 kg gives gain = (1000 − 900) ÷ 900 × 100 = 11 1/9%.

Profit and Loss Concepts

Cost Price, Selling Price, Profit and Loss

Cost price is the amount paid to obtain an article, and selling price is the amount received when it is sold. The difference between these values gives profit or loss.

CP includes the purchase cost and may also include expenses such as transport or repair when the question specifies them. If SP > CP, profit = SP − CP. If CP > SP, loss = CP − SP. If SP = CP, there is neither profit nor loss.

Example: An article bought for ₹800 and sold for ₹920 gives a profit of ₹120. If it is sold for ₹720 instead, the loss is ₹80.

Calculating Profit and Loss Percentages

Profit percentage and loss percentage are calculated by dividing the gain or loss by the cost price and multiplying by 100.

Profit% = (SP − CP) ÷ CP × 100 when SP is greater than CP. Loss% = (CP − SP) ÷ CP × 100 when CP is greater than SP. The denominator is CP, not SP, unless the question specifically asks for profit or loss as a percentage of SP.

Example: For CP = ₹1,200 and SP = ₹1,080, loss = ₹120. Therefore, loss% = 120 ÷ 1,200 × 100 = 10%.

Marked Price and Discount

Marked price is the listed price of an article, and discount is the reduction from marked price to selling price.

Discount = MP − SP and Discount% = (Discount ÷ MP) × 100. Therefore, SP after a discount of d% = MP × (100 − d) ÷ 100. A discount percentage is based on MP, whereas profit or loss percentage is generally based on CP.

Example: If MP = ₹2,000 and discount = 15%, discount = ₹300 and SP = ₹1,700.

Successive Profit, Loss and Discount

Successive percentage changes are applied one after another, so their percentages cannot usually be added directly.

For two successive changes of a% and b%, the net percentage change is a + b + (ab ÷ 100) for two increases. For an increase of a% followed by a decrease of b%, the net change is a − b − (ab ÷ 100). The sign of each percentage must match the change.

Example: A 10% discount followed by another 20% discount gives a total reduction of 10 + 20 − (10 × 20 ÷ 100) = 28%, not 30%.

Equal Selling Price Cases

When two articles are sold at equal selling prices, one at x% profit and the other at x% loss, the combined result is a loss of x² ÷ 100 percent.

For equal SP, the cost prices are SP × 100 ÷ (100 + x) and SP × 100 ÷ (100 − x). Their total cost exceeds twice the common selling price, producing a loss of x² ÷ 100 percent.

Example: If two articles are each sold for ₹1,200, one at 20% profit and one at 20% loss, the overall loss is 4%. Total CP = 1,200 × 100 ÷ 120 + 1,200 × 100 ÷ 80 = ₹2,500, while total SP = ₹2,400.

Profit and Loss Video Lessons

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CP, SP, Profit and Loss Formulas

Understand the fundamental formulas for Cost Price, Selling Price, profit and loss, including their relationships and basic calculations for quantitative aptitude.

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Practice Profit and Loss Questions

Practise published questions related to this topic.

1Find a single discount (approximately) equal to three consecutive discounts of 2%, 8% and 15%.→ 2An article is sold at a loss of 12% on its cost price. If the same article were sold for ₹84 more than its original selling price, the seller would make a profit of 8% on the same cost price. What is the cost price of the article?→ 3A shopkeeper sells an item for ₹689.7 after giving two successive discounts of 75% and 34% on its marked price. Had he not given any discount, he would have earned a profit of 76%. What is the cost price (in ₹) of the item?→ 4A grocery store gives a Buy 5, Get 2 Free offer. The price of each item is ₹300. A customer needs a total of 21 items and procures the items under this scheme. What is the effective cost per item? (Round off your answer to two decimal places.)→ 5Cost price of 10 articles is Rs. 182. Selling price of 12 articles is Rs. 182. What is the ratio of the value of profit/loss of 1 article to the cost price of 1 article? (Cost price of all the articles is same. Selling price of all the articles is same.)→ 6The marked price of an article is (7/5) of the cost price. Its selling price is (6/7) of the marked price. What is the profit percentage?→ 7Arrange the following schemes in the ascending order of their discounts. A. Buy 1 get 5 free B. A single discount of 64% C. Two successive discounts of 3% and 37%→ 8During a sale, 50% of the goods are sold at 37% profit, 30% of the remaining goods are sold at 26% profit and the still remaining goods are sold at a loss of 24%. If there is an overall profit of x%, then what is the value of x?→ 9During a sale, 55% of the goods are sold at a 41% profit, 20% of the remaining goods are sold at a 19% profit and the rest are sold at a 21% loss. If there is an overall profit of x%, then what is the value of x?→ 10A dealer purchased an AC for ₹1,848. After allowing a discount of 58% on its marked price, he still gains 63%. Find the marked price of the AC.→

Profit and Loss Quick Quiz

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Quick Revision Notes

Profit and Loss Revision Points

Use these formulas and rules for quick revision.

  • Profit = SP − CP when SP > CP.
  • Loss = CP − SP when CP > SP.
  • Profit% = Profit ÷ CP × 100.
  • Loss% = Loss ÷ CP × 100.
  • At p% profit, SP = CP × (100 + p) ÷ 100.
  • At l% loss, SP = CP × (100 − l) ÷ 100.
  • Discount = MP − SP.
  • Discount% = Discount ÷ MP × 100; its base is MP, not CP or SP generally.

Profit and Loss FAQs

What is the formula for profit percentage?

Profit% = (Profit ÷ CP) × 100, where Profit = SP − CP.

What is the formula for loss percentage?

Loss% = (Loss ÷ CP) × 100, where Loss = CP − SP.

An article is sold for ₹1,380 at a 15% profit. What is its cost price?

SP = 115% of CP. Therefore, CP = 1,380 × 100 ÷ 115 = ₹1,200.

An article with CP ₹2,500 is sold at a 12% loss. What is its selling price?

SP = 2,500 × 88 ÷ 100 = ₹2,200.

What is the difference between discount percentage and loss percentage?

Discount percentage is calculated on marked price: Discount ÷ MP × 100. Loss percentage is calculated on cost price: Loss ÷ CP × 100.

What is the overall result when articles are sold at equal selling prices, one at 25% profit and one at 25% loss?

The overall result is a loss of 25² ÷ 100 = 6.25%.

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