Profit and Loss: Formula, Percentage Explained Simply

Profit and loss describe whether a deal made or lost money. If you buy a watch for Rs. 500 (the cost price) and sell it for Rs. 650 (the selling price), you made a profit of Rs. 150. If you sold it for Rs. 420 instead, you suffered a loss of Rs. 80. Every business on Earth, from a street vendor to a giant company, runs on this single comparison.

This matters because profit and loss percentages are the universal language of business. A shopkeeper deciding what to stock, a company reporting quarterly results, and you judging whether a second-hand phone is a good deal all use the same formulas. Understanding them also protects you as a buyer: you can see through inflated discount claims and judge real value.

Key Concepts

• Cost price (CP): what the seller paid to acquire the item.
• Selling price (SP): what the buyer pays; what the seller receives.
• Profit: SP − CP, when SP is greater than CP. Loss: CP − SP, when CP is greater.
• Marked price (MP): the price tag before discount; profit and discount calculations both start from real transaction prices, not the tag alone.
• Overhead expenses: transport, repair and packaging costs are added to CP before computing profit.

Formulas

• Profit = SP − CP; Loss = CP − SP.
• Profit% = (Profit ÷ CP) x 100. Loss% = (Loss ÷ CP) x 100. Note: always on CP, never on SP.
• SP = CP x (1 + profit%/100); SP = CP x (1 − loss%/100).
• CP = SP x 100/(100 + profit%), or SP x 100/(100 − loss%).

Worked Example

A shopkeeper buys a bag for Rs. 500 and sells it for Rs. 650. Find the profit and profit%.

1. Profit = SP − CP = 650 − 500 = Rs. 150.
2. Profit% = (150 ÷ 500) x 100 = 0.3 x 100 = 30%.
3. Check: CP x (1 + 30/100) = 500 x 1.3 = Rs. 650, which matches the selling price. Correct.

Common Misconceptions

• “Profit% is calculated on the selling price.” Wrong. It is always on cost price. A Rs. 150 profit on a Rs. 650 sale is 150/500 x 100 = 30%, not 150/650 x 100.
• “A 50% profit means the price doubled.” Wrong. 50% profit on CP Rs. 100 gives SP Rs. 150. Doubling the price is a 100% profit.
• “If SP equals CP there is no profit and no loss, so it doesn't matter.” It matters: the seller's time, shop rent and effort went in for zero return, which is a real economic loss.

Real-World Applications

• Retail: shopkeepers set selling prices from wholesale cost plus a target profit%.
• Stock markets: investors track gains and losses as percentages of the purchase price.
• Everyday bargaining: knowing profit% helps you judge whether a sale price is genuinely good.

Profit is SP minus CP, loss is CP minus SP, and the percentage always divides by cost price. Fix that one habit — percent on CP — and every profit, loss and discount problem becomes a straightforward substitution into the formulas.