Percentage, Profit and Loss, Discount
Percentage, Profit and Loss, Discount
This domain tests converting between fractions, decimals and percentages, and solving profit, loss and discount problems using cost price (CP), selling price (SP) and marked price (MP).
Core rules
- Percent means “per hundred”: 35% = 35/100 = 0.35. An increase of r% gives new value = original × (1 + r/100).
- Profit = SP − CP; loss = CP − SP. Profit% = (Profit/CP) × 100; loss% = (Loss/CP) × 100.
- Discount = MP − SP; discount% = (Discount/MP) × 100. Discount is always calculated on MP.
- SP = MP × (1 − discount%/100). If profit% is given, SP = CP × (1 + profit%/100).
Worked example
An article is marked at ₹750. A 20% discount is given, and the shop still makes 25% profit. Find CP. Discount = 20% of 750 = ₹150, so SP = 750 − 150 = ₹600. Profit is 25% of CP, so SP = 1.25 × CP. Thus CP = 600 ÷ 1.25 = ₹480. Check: profit = 600 − 480 = ₹120, and 120/480 × 100 = 25%.
Traps
- Profit% and loss% are on CP, not SP or MP.
- Successive discounts of 10% and 10% give 19% total, not 20%, because the second is on the reduced price.
- A 20% discount followed by 25% profit does not mean CP = MP; work through SP.
- Do not subtract a percentage from a percentage as if they were amounts.