In this guide
Shops advertise discounts in different ways: "30% off", "20% + 10% off", "buy 2, get 1 free". SSC CHSL asks which offer is better, what a customer pays, or what profit the shopkeeper still makes after the discount. All of these rest on one rule. Discount is calculated on the marked price (MP), not on the cost price.
This topic is the profit and loss guide with one extra price added. Keep the three prices and their bases straight and every question becomes a pair of multipliers.
Three prices, two bases
| Price | What it is | Percentage measured on it |
|---|---|---|
| CP (cost price) | What the shopkeeper paid | Profit % and loss % |
| MP (marked or list price) | The price on the tag | Discount % |
| SP (selling price) | What the customer actually pays | — |
The chain runs CP → MP (marked up) → SP (discounted). Profit compares SP with CP. Discount compares SP with MP.
- Discount = MP − SP.
- Discount % = discount ÷ MP × 100.
- SP = MP × (100 − d)/100, so a 25% discount is × 0.75.
Successive discounts
Two discounts of a% and b% equal a single discount of a + b − ab/100.
Why: the second discount is taken on the already reduced price, not on the MP. The multipliers are (1 − a/100) and (1 − b/100), and their product is 1 − (a + b)/100 + ab/10,000. So the total cut is a + b − ab/100, a little less than the sum.
"20% + 10% off" is therefore 20 + 10 − 2 = 28%, not 30%. For three discounts, combine the first two, then combine the result with the third, or simply multiply all three multipliers.
Marking up to profit after a discount
A shopkeeper who wants p% profit after allowing d% discount must mark the price so that
MP/CP = (100 + p)/(100 − d)
Why: SP = CP × (100 + p)/100 from the profit side, and SP = MP × (100 − d)/100 from the discount side. Set them equal and divide.
The reverse also works. If goods are marked m% above cost and sold at d% discount, the result is a net change of m − d − md/100 on CP. It is the successive-change formula with one increase and one decrease.
"Buy x, get y free"
The customer takes x + y items and pays for x, so the effective discount is y/(x + y) × 100%.
- Buy 2, get 1 free: 1/3 = 33⅓%.
- Buy 4, get 1 free: 1/5 = 20%.
- Buy 3, get 2 free: 2/5 = 40%.
A common slip is writing y/x (1/2 = 50% for "buy 2, get 1"). The discount is on everything the customer takes home, so the denominator is x + y.
Six worked questions
Q1. A TV marked ₹30,000 is sold after successive discounts of 10% and 5%. Find the SP.
30,000 × 0.9 × 0.95 = ₹25,650. Single equivalent: 10 + 5 − 0.5 = 14.5%, and 14.5% of 30,000 is 4,350.
Q2. A shopkeeper wants a 17% profit after giving a 10% discount. How much above cost should the goods be marked?
MP/CP = 117/90 = 1.3. Mark up by 30%.
Q3. An article costing ₹500 is marked 40% above cost and sold at a 20% discount. Find the profit.
MP = 700 and SP = 700 × 0.8 = 560. Profit = ₹60, or 12%. Check with the formula: 40 − 20 − 800/100 = 12.
Q4. Goods are marked 25% above cost and a 12% discount is allowed. Find the profit percentage.
25 − 12 − 300/100 = 10%. Or 1.25 × 0.88 = 1.10.
Q5. After a 15% discount, a jacket sells for ₹1,530. Find its marked price.
SP = MP × 0.85, so MP = 1,530 ÷ 0.85 = ₹1,800.
Q6. Which is better for a customer: a single 25% discount, or successive discounts of 15% and 10%?
Successive: 15 + 10 − 1.5 = 23.5%. The single 25% discount is better.
Common mistakes
| Mistake | Fix |
|---|---|
| Taking discount on CP | Discount is on MP |
| Adding successive discounts | Use a + b − ab/100 |
| Mixing the bases (profit on MP) | Profit is on CP, discount on MP |
| "Buy 2 get 1" as 50% | Divide by all items taken: 1/3 |
| Finding MP by adding the discount back to SP | Divide SP by the multiplier (1 − d/100) |
Practice
- A bag marked ₹2,500 is sold for ₹2,000. Find the discount percentage.
- Find the single discount equivalent to successive discounts of 30% and 20%.
- At what percentage above cost should an article be marked to earn 20% profit after a 20% discount?
- What is the effective discount in "buy 3, get 2 free"?
- An article marked ₹800 is sold at a 15% discount, giving a profit of 13⅓%. Find its cost price.
- Find the selling price of an item marked ₹5,000 after successive discounts of 10%, 20% and 10%.
- A shopkeeper allows a 10% discount and still gains 8%. The cost price is ₹500. Find the marked price.
- On a ₹2,000 item, which is better: 30% off, or 20% off followed by 15% off? By how much?
Answers:
- 20%. Discount 500 on 2,500.
- 44%. 30 + 20 − 600/100.
- 50%. MP/CP = 120/80 = 1.5.
- 40%. 2/(3 + 2) × 100.
- ₹600. SP = 800 × 0.85 = 680. CP = 680 ÷ (17/15) = 600, since 113⅓% is 17/15.
- ₹3,240. 5,000 × 0.9 × 0.8 × 0.9. The single equivalent is 35.2%.
- ₹600. SP = 500 × 1.08 = 540, and MP = 540 ÷ 0.9 = 600.
- 20% then 15%, by ₹40. That offer is 20 + 15 − 3 = 32%, so the price is ₹1,360, against ₹1,400 for 30% off.
What to do next
- Draw the CP → MP → SP chain once and label which percentage sits on which base.
- Solve 15 successive-discount questions using only the formula, then 5 by multiplying, to check.
- Practise five "mark up then discount" questions a day for a week, and time them.
- Revise percentages if the multipliers still feel slow, then move on to simple and compound interest.
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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