Cost Price and Selling Price: Formulas, Rules and Examples

Cost Price and Selling Price are the two basic values used in profit and loss calculations. Cost Price is the amount paid to purchase an item, while Selling Price is the amount received when it is sold. Comparing CP and SP determines whether the transaction results in profit, loss or no profit and no loss.

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What are Cost Price and Selling Price?

Cost Price (CP) is the amount paid by a seller to acquire an article. Selling Price (SP) is the amount at which the article is sold to a buyer.

If SP is greater than CP, the seller makes a profit. If SP is less than CP, the seller incurs a loss. When SP equals CP, there is neither profit nor loss. For example, if an article is bought for ₹800 and sold for ₹920, CP = ₹800, SP = ₹920 and profit = ₹120.

Cost Price and Selling Price Formula & Tricks

Important Formulas

Profit
Profit = SP − CP

Profit occurs when the selling price is greater than the cost price.

Loss
Loss = CP − SP

Loss occurs when the cost price is greater than the selling price.

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

Profit percentage is always calculated on the cost price.

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

Loss percentage is calculated on the cost price.

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

Use this formula when CP and the required profit percentage are given.

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

Use this formula when CP and the loss percentage are given.

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

Use this reverse formula when SP and profit percentage are known.

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

Use this reverse formula when SP and loss percentage are known.

Quick Tricks

Use the 100-based ratio

At a profit of p%, CP:SP = 100:(100 + p). At a loss of l%, CP:SP = 100:(100 − l). This avoids writing separate percentage calculations.

Example: For a 20% profit, CP:SP = 100:120 = 5:6. If CP is ₹500, SP = ₹500 × 6/5 = ₹600.
Find percentage from the difference

First find the difference between SP and CP. Divide this difference by CP, not SP, and multiply by 100.

Example: If CP = ₹750 and SP = ₹690, loss = ₹60. Loss% = (60/750) × 100 = 8%.
Check the result using the price comparison

A profit answer must have SP greater than CP, while a loss answer must have SP less than CP. This sign check can identify a reversed formula.

Example: For CP = ₹1,200 and loss = 15%, SP = 1,200 × 85/100 = ₹1,020, which is correctly less than CP.

Cost Price and Selling Price Concepts

Identifying Profit, Loss and No Profit No Loss

Compare SP with CP to determine the result of a sale.

If SP > CP, Profit = SP − CP. If CP > SP, Loss = CP − SP. If SP = CP, the transaction has no profit and no loss.

Example: For CP = ₹450 and SP = ₹500, profit = ₹500 − ₹450 = ₹50. For CP = ₹450 and SP = ₹400, loss = ₹450 − ₹400 = ₹50.

Calculating Selling Price from Cost Price

The selling price is found by increasing or decreasing CP according to the profit or loss percentage.

For p% profit, SP = CP × (100 + p)/100. For l% loss, SP = CP × (100 − l)/100. The percentage change is applied to CP.

Example: If CP = ₹2,400 and profit = 15%, SP = 2,400 × 115/100 = ₹2,760.

Calculating Cost Price from Selling Price

Cost price can be recovered from SP by reversing the profit or loss percentage calculation.

For p% profit, CP = SP × 100/(100 + p). For l% loss, CP = SP × 100/(100 − l). The denominator changes because the given percentage is based on CP.

Example: If SP = ₹1,380 after a 15% profit, CP = 1,380 × 100/115 = ₹1,200.

Profit and Loss Percentages Use CP as the Base

Profit percentage and loss percentage are calculated using CP as the denominator.

Profit% = (SP − CP)/CP × 100 when SP > CP. Loss% = (CP − SP)/CP × 100 when CP > SP. Dividing by SP gives a different percentage and is not the standard profit-loss percentage.

Example: For CP = ₹500 and SP = ₹600, profit = ₹100 and profit% = 100/500 × 100 = 20%, not 100/600 × 100.

Cost Price and Selling Price 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 Cost Price and Selling Price Questions

Practise published questions related to this topic.

1A person sells an article at the profit of 50 percent. Cost price and selling price are increased by 40 percent and 'y' percent respectively. If the new profit percentage is 75 percent, then what is the value of 'y'?→ 2Selling price of an article is Rs. 510. Loss percentage is 15 percent. What is the cost price of the article?→ 3Find the single equivalent discount (rounded off to two decimal places) for successive discounts of 18%, 6% and 25%.→ 4A store offers a 10% festival discount on the marked price of ₹900. Later, to clear the stock, it offers an additional 5% off on the already discounted price. What is the total amount paid by the customer?→ 5If the listed price of a bag is 85% more than its cost price and a discount of 49% is announced on it, then find the loss percentage.→ 6The cost price of 28 mangoes is the same as the selling price of 25 mangoes. Find the profit percentage.→ 7The marked price of an article is 25 percent more than its cost price. If the profit earned is 18 percent, then what is the discount offered on the article?→ 8A trader buys an item for ₹500 and gains 20%. What is the selling price?→ 9An article marked at ₹1,250 is sold at two successive discounts such that the selling price becomes ₹900. If the first discount is 20%, what is the second discount?→ 10A shopkeeper fixed the marked price of an article as ₹2,40,000. He gave 30% and 18% successive discounts on one article and 48% discount on another article of the same marked price. On which of the two articles did the shopkeeper get more benefit and how much more was it?→

Cost Price and Selling Price Quick Quiz

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Quick Revision Notes

Cost Price and Selling Price: Quick Revision

Use these rules to solve direct and reverse CP-SP questions.

  • CP is the purchase price and SP is the sale price.
  • SP > CP indicates profit; CP > SP indicates loss; SP = CP indicates no profit and no loss.
  • Profit = SP − CP and Loss = CP − SP.
  • Profit% and Loss% are calculated on CP.
  • For p% profit, SP = CP × (100 + p)/100.
  • For l% loss, SP = CP × (100 − l)/100.
  • For p% profit, CP = SP × 100/(100 + p).
  • For l% loss, CP = SP × 100/(100 − l).

Cost Price and Selling Price FAQs

What is the cost price formula when selling price and profit percentage are given?

CP = SP × 100/(100 + Profit%). For example, if SP = ₹960 at a 20% profit, CP = 960 × 100/120 = ₹800.

What is the selling price formula for a loss?

SP = CP × (100 − Loss%)/100. If CP = ₹1,500 and loss = 12%, SP = 1,500 × 88/100 = ₹1,320.

A product has CP ₹640 and SP ₹800. What is the profit percentage?

Profit = ₹800 − ₹640 = ₹160. Profit% = (160/640) × 100 = 25%.

A product has CP ₹900 and SP ₹765. What is the loss percentage?

Loss = ₹900 − ₹765 = ₹135. Loss% = (135/900) × 100 = 15%.

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

There is no profit and no loss. Profit or loss is ₹0, and the profit-loss percentage is 0%.

Why is profit percentage calculated on cost price rather than selling price?

The standard profit percentage compares the gain with the amount invested, so Profit% = Profit/CP × 100. For CP ₹400 and SP ₹500, the profit is 25% of CP.

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