In this guide
Profit and loss questions are really percentage questions in a shop. Once you see that selling price is simply cost price multiplied by a factor, and that a discount is a percentage decrease on the marked price, most questions reduce to one or two multiplications. The difficulty lies in keeping track of which price is the base for each percentage.
The three prices
| Term | Meaning |
|---|---|
| Cost price (CP) | What the seller paid |
| Marked price (MP) | The price on the label (list price) |
| Selling price (SP) | What the buyer actually pays |
- Profit or loss is calculated on CP.
- Discount is calculated on MP.
The multiplier method
- SP = CP × (1 + profit%/100), or CP × (1 − loss%/100).
- SP = MP × (1 − discount%/100).
Worked example: An article costing ₹600 is sold at a 15% profit. SP = 600 × 1.15 = ₹690.
Markup and discount together
Worked example: A shopkeeper marks goods 40% above cost and gives a 20% discount. What is the profit percentage?
Let CP = 100. MP = 140. SP = 140 × 0.8 = 112. Profit = 12%.
A useful relation: MP/CP = (100 + profit%)/(100 − discount%).
Worked example: At what percentage above cost must an article be marked so that, after a 25% discount, the profit is 20%?
MP/CP = 120/75 = 1.6, so the article must be marked 60% above cost.
Successive discounts
Discounts of a% and b% in succession equal a single discount of:
a + b − (ab/100)
Worked example: Successive discounts of 20% and 10% = 20 + 10 − 2 = 28%.
Dishonest dealers and false weights
If a trader claims to sell at cost price but uses a false weight, the profit % is:
(error ÷ weight actually given) × 100
Worked example: A shopkeeper uses a 900 g weight instead of 1 kg and sells at cost price.
Profit = 100/900 × 100 = 11.11%.
If the trader also adds a profit on top, multiply the factors: selling at 10% profit with a 900 g weight gives 1.1 × (1000/900) = 1.2222, a profit of 22.22%.
Two articles, same selling price
If two articles are each sold at the same SP, one at x% profit and the other at x% loss, there is always an overall loss of:
x²/100 %
Worked example: Two phones are sold at ₹12,000 each, one at 20% profit and one at 20% loss. Overall loss = 400/100 = 4%.
"Buy x, get y free"
The effective discount = y/(x + y) × 100%.
Worked example: "Buy 3, get 1 free" = 1/4 × 100 = 25% discount.
Finding CP from the selling price
Worked example: By selling an article for ₹1,080, a trader gains 20%. Find the CP.
CP = 1,080 ÷ 1.2 = ₹900.
Worked example: A trader loses 10% by selling at ₹540. At what price should it be sold to gain 10%?
CP = 540 ÷ 0.9 = 600; required SP = 600 × 1.1 = ₹660.
Common traps
| Trap | Correct approach |
|---|---|
| Calculating profit on SP | Profit is on CP unless stated otherwise |
| Adding successive discounts | Use a + b − ab/100 |
| Discount on CP | Discount is on MP |
| Assuming "same SP" means no loss | There is always a loss of x²/100 % |
Practice
- An article bought for ₹750 is sold for ₹900. Find the profit percentage.
- A trader marks goods 25% above CP and gives a 12% discount. Find the profit percentage.
- Find the single discount equivalent to successive discounts of 25% and 20%.
- A dealer sells at cost price but uses a weight of 950 g for 1 kg. Find the profit percentage.
- Two articles are sold for ₹990 each, one at 10% profit and one at 10% loss. Find the overall result.
- At what percentage above CP should an article be marked so that after a 10% discount the profit is 17%?
Answers: 1. 20%. 2. 10%. 3. 40%. 4. 5.26% (50/950). 5. 1% loss. 6. 30%.
A note on dates and numbers. Exam patterns, vacancies and schedules change from year to year. Always confirm the current details in the latest notification on the Staff Selection Commission website .
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