Profit and Loss Formulas and Tricks with Examples
Profit and loss is one of the most common topics in Indian school maths and in aptitude tests for banking, SSC and other competitive exams. It is based on everyday buying and selling, so once you learn a few formulas and shortcuts, the questions become easy marks. This guide covers cost price, selling price, profit percentage, loss percentage and quick tricks with worked examples.
Cost price and selling price
Every profit and loss question is built on two ideas.
- Cost price (CP): the price at which an item is bought.
- Selling price (SP): the price at which the item is sold.
If SP is greater than CP, there is a profit. If SP is less than CP, there is a loss. The basic formulas are Profit = SP − CP and Loss = CP − SP.
Profit% and loss% formulas
Percentages are always calculated on the cost price. The formulas are Profit% = (Profit / CP) × 100 and Loss% = (Loss / CP) × 100.
Example: A shopkeeper buys a bag for ₹500 and sells it for ₹600. Profit = 600 − 500 = ₹100. Profit% = (100 / 500) × 100 = 20%.
Example: A phone bought for ₹800 is sold for ₹680. Loss = 800 − 680 = ₹120. Loss% = (120 / 800) × 100 = 15%.
Finding SP or CP directly
You can jump straight to the answer with these forms: SP = CP × (100 + Profit%) / 100 for a gain, and CP = SP × 100 / (100 + Profit%) to work backwards.
Example: An item costs ₹1,200 and is sold at a 25% profit. SP = 1200 × (100 + 25) / 100 = 1200 × 1.25 = ₹1,500.
Example: An item is sold for ₹1,500 at a 25% profit. Its cost price = 1500 × 100 / 125 = ₹1,200, confirming the reverse works.
Handy shortcuts for exams
One popular trick: if two items are sold at the same selling price, one at x% profit and the other at x% loss, there is always an overall loss of (x/10)% squared. For x = 20, the net loss is (20/10)² = 4%, no matter what the prices are. Another tip is to remember that profit and loss are percentages of CP, never SP, which is the most common mistake students make.
Because this topic is pure percentage work, our fractions, decimals and percentages guide is a great companion, and you can pick up more speed hacks in our fun maths tricks for students. Students building toward advanced exams can also visit our JEE Maths section for higher-level practice.
Frequently asked questions
Is profit percentage calculated on cost price or selling price?
Profit percentage and loss percentage are always calculated on the cost price, not the selling price. Using selling price by mistake is the single most common error in profit and loss questions, so always divide by CP.
How do I find cost price when profit percentage is given?
Use CP = SP × 100 / (100 + Profit%). For example, if an item sells for ₹660 at a 10% profit, then CP = 660 × 100 / 110 = ₹600, which is the original cost price.
If equal-priced items are sold at the same profit% and loss%, is it break-even?
No, it results in an overall loss. When two items are sold at the same price, one at x% gain and one at x% loss, the net result is always a loss of (x/10)% squared, for example 4% when x is 20.