In this guide
In a shop, the price on the label is the marked price (MP). When the shop offers a discount, you pay less. That lower amount is the selling price (SP).
SP = MP − Discount
Discount questions are close cousins of profit and loss. The difference is the base: profit is counted on the cost price, while discount is counted on the marked price. Keep those two bases straight and this chapter is mostly quick percentage work.
Three prices, two bases
| Price | Who sets it | Percentages counted on it |
|---|---|---|
| Cost price (CP) | What the shopkeeper paid | Profit %, loss %, mark-up % |
| Marked price (MP) | The label price | Discount % |
| Selling price (SP) | What the customer pays | None: it is the result |
The formulas
- Discount = MP − SP
- Discount % = discount ÷ MP × 100
- SP = MP × (100 − discount %) ÷ 100
- MP = SP × 100 ÷ (100 − discount %)
A 20% discount means SP = 0.8 × MP. To go back from SP to MP, divide by 0.8.
Two discounts in a row
When two discounts are given one after another, the second is taken on the already reduced price, not on the MP.
Single equivalent discount for a% and b% = a + b − (a × b ÷ 100)
| Two discounts | Single equivalent |
|---|---|
| 10% and 10% | 19% |
| 20% and 10% | 28% |
| 20% and 20% | 36% |
| 25% and 20% | 40% |
| 10% and 5% | 14.5% |
The order of the two discounts does not matter. 20% then 10% gives the same final price as 10% then 20%.
Buy and get free
In "buy x, get y free", you take home x + y items and pay for x.
Discount % = y ÷ (x + y) × 100
"Buy 1, get 1 free" is 50%. "Buy 3, get 1 free" is 25%, not 33⅓%, because the free item is 1 out of 4 items taken.
Discount and profit together
A shopkeeper often marks goods above cost, then offers a discount, and still makes a profit. The chain is:
CP → (mark up) → MP → (discount) → SP
To find what MP gives a profit of p% after a discount of d%:
MP = CP × (100 + p) ÷ (100 − d)
Solved examples
Example 1. A jacket marked ₹2,400 is sold for ₹1,980. Find the discount percentage.
- Discount = 2,400 − 1,980 = ₹420.
- Discount % = 420 ÷ 2,400 × 100 = 17.5%.
Example 2. A cooler marked ₹3,500 is sold at a 15% discount. Find the selling price.
- SP = 3,500 × 0.85.
- SP = ₹2,975.
Example 3. After a 20% discount, a bag sells for ₹1,440. Find its marked price.
- SP = 0.8 × MP.
- MP = 1,440 ÷ 0.8 = ₹1,800.
- Check: 20% of 1,800 = 360, and 1,800 − 360 = 1,440.
Example 4. A TV marked ₹5,000 is sold after successive discounts of 20% and 10%. Find the SP and the single equivalent discount.
- After 20%: 5,000 × 0.8 = ₹4,000.
- After 10% on ₹4,000: 4,000 × 0.9 = ₹3,600.
- Single equivalent = 20 + 10 − (20 × 10 ÷ 100) = 28%. Check: 28% of 5,000 = 1,400, and 5,000 − 1,400 = 3,600.
Example 5. A shop offers "buy 2, get 1 free". Find the effective discount.
- You take 3 items and pay for 2.
- Discount = 1 ÷ 3 × 100 = 33⅓%.
Example 6. An article costs ₹600. It is marked 40% above cost and sold at a 10% discount. Find the profit percentage.
- MP = 600 × 1.4 = ₹840.
- SP = 840 × 0.9 = ₹756.
- Profit = 756 − 600 = ₹156, which is 156 ÷ 600 × 100 = 26%.
Example 7. An article costs ₹900. At what price should it be marked so that after a 10% discount the shopkeeper still gains 20%?
- MP = 900 × 120 ÷ 90.
- MP = ₹1,200.
- Check: 10% off ₹1,200 gives ₹1,080, and 1,080 = 900 × 1.2.
Common mistakes
| Mistake | Correct way |
|---|---|
| Discount % on cost price | Discount % is on the marked price |
| 20% + 10% = 30% discount | Successive: 28% |
| "Buy 3, get 1 free" = 33⅓% | 1 free out of 4 taken = 25% |
| MP = SP + 20% of SP | MP = SP ÷ 0.8 |
| Mixing up mark-up % and profit % | Mark-up is on CP before the discount; profit is on CP after it |
Practice set
- An item marked ₹1,600 is sold for ₹1,360. Find the discount percentage.
- A phone marked ₹4,200 is sold at a 12% discount. Find the SP.
- After a 15% discount, an item sells for ₹1,700. Find the MP.
- Find the single discount equal to two successive discounts of 10% and 10%.
- An item marked ₹8,000 gets successive discounts of 25% and 20%. Find the SP.
- Find the discount in "buy 3, get 2 free".
- An article costing ₹500 is marked 30% above cost and sold at a 10% discount. Find the profit percentage.
- An article costs ₹1,200. What should its MP be so that after a 20% discount the profit is 20%?
Answers:
- Discount ₹240; 240 ÷ 1,600 × 100 = 15%.
- 4,200 × 0.88 = ₹3,696.
- 1,700 ÷ 0.85 = ₹2,000.
- 10 + 10 − 1 = 19%.
- 8,000 × 0.75 = 6,000; 6,000 × 0.8 = ₹4,800.
- 2 free out of 5 taken: 2 ÷ 5 × 100 = 40%.
- MP ₹650; SP 650 × 0.9 = ₹585; profit ₹85 on ₹500 = 17%.
- 1,200 × 120 ÷ 80 = ₹1,800. Check: 20% off gives ₹1,440 = 1,200 × 1.2.
What to do next
- Say aloud, for each question, which base it uses: CP or MP.
- Learn the successive-discount table and the buy-and-get formula.
- Mix 10 discount questions with 10 profit and loss questions in one sitting.
- Revise successive changes in our percentage guide; the idea is the same.
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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