Profit, loss and discount
Profit and loss are always measured on the cost price, and discount is always measured on the marked price. Every question comes down to turning each step into a multiplying factor and keeping track of which price is the base.
Formulas and when they apply
- Profit = SP − CP and Loss = CP − SP, where SP is the selling price and CP is the cost price
- Profit % = Profit ÷ CP × 100 and Loss % = Loss ÷ CP × 100
- SP = CP × (1 + profit/100) for a profit, SP = CP × (1 − loss/100) for a loss
- Discount = marked price − SP, and Discount % = Discount ÷ marked price × 100
- Two successive discounts of a% and b% equal one discount of a + b − ab/100 (%)
- Marked price = CP × (1 + profit/100) ÷ (1 − discount/100)Applies when: discount allowed on the marked price
- Two items sold at the same price, one at x% gain and one at x% loss, give a net loss of x²/100 percent of the total costApplies when: equal selling prices and equal percents
- Profit % with a false weight = (true weight − false weight) ÷ false weight × 100Applies when: goods sold at cost price per unit
Worked examples
Example 1. A shopkeeper buys an item for ₹ 600, marks it 50% above cost and gives a 20% discount. What is his profit percent?
Solution. Marked price = 600 × 1.50 = ₹ 900. Discount = 20% of 900 = ₹ 180, so SP = ₹ 720. Profit = 720 − 600 = ₹ 120. Profit % = 120 ÷ 600 × 100 = 20%.
Example 2. What single discount equals two successive discounts of 10% and 5%?
Solution. Take the price as 100. After 10% off it is 90. After 5% off 90 it is 90 × 0.95 = 85.5. The single discount is 100 − 85.5 = 14.5%.
Example 3. A trader sells an article for ₹ 1,150 and gains 15%. What did it cost him?
Solution. SP is 115% of the cost price, so CP = 1,150 ÷ 1.15 = ₹ 1,000.
Shortcuts and their limits
- Turn every step into a factor: markup 1.5, discount 0.8, so SP = CP × 1.5 × 0.8 = 1.2 × CP.Does not apply when: Works only when each percent is on the price from the step before. Check which base each percent uses.
- For equal-price items sold at x% gain and x% loss, the loss is x²/100 percent of the total cost.Does not apply when: It does not apply when the selling prices are different or the percents are not equal.
- For a false weight with goods sold at cost price per unit, profit % = error ÷ (true weight − error) × 100.Does not apply when: It assumes the trader buys with the correct weight and sells with the wrong one.
Common mistakes
- Calculating profit or loss percent on the selling price instead of the cost price.
- Taking discount on the cost price instead of the marked price.
- Adding successive discounts or profits instead of multiplying their factors.
- Believing equal percent gain and loss cancel out when the cost prices differ.
- Forgetting to find the cost price first when the question gives only a selling price and a loss or profit percent.
Independent practice made by EduVistaHQ with original questions. It is not an official examination paper, it is not affiliated with or endorsed by any examination body or company, and a practice score does not predict a real result.