Simple Profit and Loss: Basic Formulas, Rules and Examples

Simple Profit and Loss deals with cost price, selling price, gain, loss and their percentages. Cost price is the purchase value, while selling price is the value received on sale. The basic calculations use the difference between these prices and express profit or loss as a percentage of cost price.

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What is Simple Profit and Loss?

Simple Profit and Loss compares the cost price of an article with its selling price. Selling above the cost price gives profit, while selling below the cost price gives loss.

Cost Price (CP) is the amount paid to purchase an article, and Selling Price (SP) is the amount received on selling it. If SP > CP, Profit = SP − CP. If SP < CP, Loss = CP − SP. Profit or loss percentage is calculated on CP unless another base is specifically stated. For example, if CP is ₹500 and SP is ₹575, profit is ₹75 and profit percentage is 15%.

Simple Profit and Loss Formula & Tricks

Important Formulas

Profit
Profit = SP − CP, when SP > CP

Profit is the excess of the selling price over the cost price.

Loss
Loss = CP − SP, when CP > SP

Loss is the excess of the cost price over 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 at Profit
SP = CP × (100 + Profit%) ÷ 100

Use this formula when cost price and profit percentage are given.

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

Use this formula when cost price and loss percentage are given.

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

Use this reverse formula when selling price and profit percentage are known.

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

Use this reverse formula when selling price and loss percentage are known.

Quick Tricks

Assume CP as 100 for percentage-only questions

When only profit or loss percentages are compared and no actual price is given, take CP = 100. The selling price becomes 100 + profit percentage or 100 − loss percentage.

Example: At 20% profit, CP = 100 and SP = 120. At 20% loss, CP = 100 and SP = 80.
Keep the percentage base as CP

Profit and loss percentages are normally calculated on cost price, not selling price. First find the rupee profit or loss, then divide by CP.

Example: If CP = ₹800 and SP = ₹920, profit = ₹120 and profit% = 120/800 × 100 = 15%, not 120/920 × 100.
Use multipliers for direct calculation

A profit of p% changes CP to CP × (1 + p/100), while a loss of l% changes CP to CP × (1 − l/100).

Example: For CP ₹1,200 and 15% loss, SP = 1,200 × 0.85 = ₹1,020.

Simple Profit and Loss Concepts

Cost Price, Selling Price, Profit and Loss

Cost price is the purchase amount and selling price is the sale amount. Their difference determines whether the transaction gives profit or loss.

If SP is greater than CP, Profit = SP − CP. If CP is greater than SP, Loss = CP − SP. If SP equals CP, there is neither profit nor loss. For CP ₹750 and SP ₹900, profit = ₹150.

Example: For CP = ₹750 and SP = ₹900: Profit = 900 − 750 = ₹150.

Calculating Profit and Loss Percentage

Profit or loss percentage is the corresponding gain or loss divided by cost price and multiplied by 100.

Profit% = (Profit/CP) × 100 and Loss% = (Loss/CP) × 100. The denominator remains CP because the percentage measures the change relative to the purchase amount.

Example: If CP = ₹2,000 and loss = ₹240, Loss% = 240/2,000 × 100 = 12%.

Finding Selling Price from Cost Price

For a given profit, add the profit percentage to 100; for a given loss, subtract the loss percentage from 100.

At p% profit, SP = CP × (100 + p)/100. At l% loss, SP = CP × (100 − l)/100. If CP = ₹1,500 and profit = 12%, SP = 1,500 × 112/100 = ₹1,680.

Example: If CP = ₹1,500 and loss = 8%, SP = 1,500 × 92/100 = ₹1,380.

Finding Cost Price from Selling Price

When selling price and the percentage are known, divide SP by the appropriate selling-price multiplier to find CP.

At p% profit, CP = SP × 100/(100 + p). At l% loss, CP = SP × 100/(100 − l). For SP ₹1,260 at 5% profit, CP = 1,260 × 100/105 = ₹1,200.

Example: For SP = ₹1,140 at 5% loss, CP = 1,140 × 100/95 = ₹1,200.

Profit or Loss Ratio

The ratio of profit or loss to cost price gives the corresponding percentage after multiplication by 100.

Profit : CP = Profit% : 100, and Loss : CP = Loss% : 100. If profit is ₹180 on CP ₹1,200, the ratio is 180:1,200 = 3:20, which equals 15%.

Example: A loss of ₹90 on CP ₹600 gives Loss:CP = 90:600 = 3:20, so loss = 15%.

Simple 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 Simple Profit and Loss Questions

Practise published questions related to this topic.

1If the expenditure of Company A in 2023 was ₹660 crore and the profit percentage was 35%, then what was its income in 2023?7052→ 2By selling lemons at 5 for a rupee, a man loses 34%. To gain 10% how many must he sell for a rupee?→ 3The 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?→ 4Cost price of an article is Rs. 450. The profit percentage is 20 percent. What is the value of profit?→ 5The cost price of 12 articles is the same as the selling price of 8 articles. What is the profit percent?→ 6If the selling price of a bed is 6 times the initial selling price, the profit is 9 times the initial profit. Find the initial profit percentage.→ 7The marked price of an article is 120 percent of its cost price. Its selling price is 90 percent of the marked price. What is the profit percentage?→ 8By selling an article for ₹117 , a man loses 40% . At what price (in ₹ ) should he sell the same article to gain 40% ?→ 9If a trader purchases 50 notebooks for ₹1000 and sells all at a gain of 20%, what is the selling price of each notebook?→ 10A person earns 25 percent profit on selling price. What is the ratio of the value of the profit to the cost price of the article?→

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Quick Revision Notes

Simple Profit and Loss Revision Points

Use these direct rules and formulas for basic calculations.

  • CP is the purchase price and SP is the selling price.
  • 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.
  • At p% profit, CP = SP × 100/(100 + p). At l% loss, CP = SP × 100/(100 − l).

Simple Profit and Loss FAQs

What is the basic profit and loss formula?

Profit = SP − CP when SP is greater than CP, and Loss = CP − SP when CP is greater than SP. Profit or loss percentage = corresponding amount ÷ CP × 100.

A product costs ₹800 and is sold for ₹920. What is the profit percentage?

Profit = ₹920 − ₹800 = ₹120. Profit% = 120/800 × 100 = 15%.

An article is sold at 20% loss for ₹640. What is its cost price?

CP = SP × 100/(100 − 20) = 640 × 100/80 = ₹800.

What is the selling price of an article costing ₹2,500 when the profit is 16%?

SP = 2,500 × 116/100 = ₹2,900.

If CP and SP are equal, what is the result?

There is neither profit nor loss, because SP − CP = 0.

On which price is profit or loss percentage normally calculated?

It is normally calculated on cost price. For example, a ₹100 profit on CP ₹500 is 100/500 × 100 = 20%.

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