The core relations
- Profit = SP − CP; loss = CP − SP.
- Profit % = profit ÷ CP × 100; loss % = loss ÷ CP × 100. The base is always the cost price.
- SP = CP × (1 + profit%) or CP × (1 − loss%).
- Markup and discount: the marked price (MP) is set above cost; a discount is a percentage of the MP, and SP = MP × (1 − discount%).
If you are comfortable with percentage, this topic is mostly about choosing the right base.
Worked examples
Example 1. An article bought for 400 is sold for 460. Profit = 60; profit % = 60 ÷ 400 = 15%.
Example 2. A trader marks an item 25% above cost and gives a 20% discount. Taking CP as 100: MP = 125, SP = 125 × 0.8 = 100. Profit is 0%.
Example 3. By selling at 540, a seller makes a 20% profit. The cost price is 540 ÷ 1.2 = 450.
Example 4. Two articles are sold at 1,200 each; one at a 20% profit, the other at a 20% loss. Overall? The first has CP = 1,200 ÷ 1.2 = 1,000; the second has CP = 1,200 ÷ 0.8 = 1,500. Total CP = 2,500; total SP = 2,400; loss = 100, which is 4% of 2,500. (When two items are sold at the same price with equal profit and loss percentages, there is always an overall loss.)
Example 5. Successive discounts of 20% and 10% on a marked price of 500: 500 × 0.8 × 0.9 = 360. The single equivalent discount is 28%, not 30%.
Common traps
- Taking profit on the selling price instead of the cost price.
- Adding discounts: 20% and 10% is 28% in total, not 30%.
- Using the same percentage for profit and loss as if they cancel. They do not.
- Applying a discount to the cost instead of the marked price.
Speed tips
- Assume CP = 100 when only percentages are given.
- Use multiplying factors for SP, MP and discounts.
- For false-weight problems, profit % = (error ÷ true weight used) × 100: a trader who uses 900 g for a kilogram gains 100 ÷ 900 = 11.1%.
A practice routine
- Day 1: CP, SP and profit % with ten direct questions.
- Day 2: markup and discount, ten questions with CP = 100.
- Day 3: successive discounts and equal-price problems.
- Day 4: a timed set of 15 mixed questions at 50 seconds each.
- Day 5: review; add the base trap to your error log.
Where it appears
Profit and loss is a standard in SSC CGL, banking, railway mathematics and MAT Mathematical Skills. It also feeds into simplification and data interpretation.
Where to go next
Move on to simple interest, ratio and proportion and a mixed timed set. Tests below are published by institutes and educators on TestMint.
