Discount and Marked Price: Successive Discounts, Offers and Markup
Discount and Marked Price: Successive Discounts, Offers and Markup
Discount questions are the most-repeated Profit-Loss family in the 2025-26 NTPC papers: markup plus discount, successive discounts, "buy x get y free" with an extra discount, and the markup needed for a target profit. Discount is always on the MARKED price; profit is always on the COST price. Keep those two bases apart and every question becomes a product of factors.
1. Formula Box
Discount = MP − SP Discount % = Discount/MP × 100 SP = MP × (100 − d)/100
MP/CP = (100 + profit %)/(100 − discount %)
Markup m% then discount d%: net profit % = m − d − md/100
| Term | Base | Example |
|---|---|---|
| Markup % | On CP | CP ₹1,500 marked 30% up gives MP ₹1,950 |
| Discount % | On MP | 15% off ₹1,950 gives SP ₹1,657.50 |
| Profit % | On CP | 1,657.50 vs 1,500 is 10.5% profit |
2. Successive Discounts and Offers
Two successive discounts d₁ and d₂ = single discount of d₁ + d₂ − d₁d₂/100
Three or more: single discount = 100 − 100 × (1 − d₁/100)(1 − d₂/100)(1 − d₃/100)
Buy x get y free: discount = y/(x + y) × 100
| Successive discounts | Single equivalent |
|---|---|
| 10%, 10% | 19% |
| 20%, 10% | 28% |
| 15%, 15% | 27.75% |
| 20%, 15% | 32% |
| 10%, 10%, 10% | 27.1% |
| 10%, 20%, 25% | 46% |
The ORDER of successive discounts does not matter (20% then 10% equals 10% then 20%), but a single discount equal to their SUM is always better for the buyer. On an MP of ₹8,000: a single 30% saves ₹2,400, 20% + 10% saves ₹2,240 and 15% + 15% saves ₹2,220.
| Offer | Effective discount |
|---|---|
| Buy 1 get 1 free | 50% |
| Buy 2 get 1 free | 33⅓% |
| Buy 3 get 1 free | 25% |
| Buy 4 get 1 free | 20% |
| Buy 3 get 2 free | 40% |
| ₹3 off on every ₹40 | 7.5% |
✗ 20% and 10% successive = 30% | ✓ The second discount is on the reduced price: 20 + 10 − 2 = 28%
✗ Discount % = discount/CP × 100 | ✓ Discount is always on the marked price
हिंदी नोट: छूट हमेशा अंकित मूल्य (MP) पर और लाभ हमेशा क्रय मूल्य (CP) पर निकलता है। दो क्रमागत छूटों का एकल समतुल्य d₁ + d₂ − d₁d₂/100 होता है; "x खरीदो y मुफ्त" में छूट y/(x + y) × 100 होती है।
Exam Pointer: Verified NTPC patterns, nearly all from the 2025-26 cycle: markup then discount for net profit (June 2025 Graduate CBT-1, June 2026 UG CBT-1), single equivalent of successive discounts and single-vs-successive differences (August 2025, May 2026 and June 2026 UG CBT-1), buy-x-get-y-free with an extra discount (August 2025 UG CBT-1, March 2026 Graduate CBT-1), markup needed for a target profit (June 2025 and March 2026 Graduate CBT-1) and the additional discount after a sale discount (June 2026 UG CBT-1). The MP-to-CP ratio pattern is tagged syllabus-based.
Pariksha Pattern: Every Way NTPC Asks This Topic
Pattern 1: Markup and discount: net profit
[PYQ: NTPC Graduate CBT-1 5-Jun-2025 Shift-3 | NTPC UG CBT-1 15-Jun-2026 Shift-2]
EXAM LEVEL
Q. An article costing ₹1,500 is marked 30% above cost and sold at a 15% discount. Find the selling price and the profit percent.
MP = 1,500 × 1.3 = ₹1,950. SP = 1,950 × 0.85 = ₹1,657.50. Profit % = 30 − 15 − (30 × 15)/100 = 10.5%. Check: 157.50/1,500 = 10.5%.
Answer: SP ₹1,657.50; profit 10.5%
EXAMATLAS LEVEL
Q. A retailer marks his goods 25% above cost price and allows a discount of ₹3 on every ₹40 of the marked price. Find his gain percent.
₹3 on ₹40 is a 7.5% discount. Net factor = 1.25 × 0.925 = 1.15625, so the gain is 15.625%. Treating ₹3 per ₹40 as 3% or as a flat ₹3 off the whole bill are the two traps.
Answer: 15.625%
Pattern 2: Successive discounts: single equivalent and differences
[PYQ: NTPC UG CBT-1 7-May-2026 Shift-2 | NTPC UG CBT-1 13-Aug-2025 Shift-1 | NTPC UG CBT-1 14-Jun-2026 Shift-3]
EXAM LEVEL
Q. Find the single discount equivalent to successive discounts of 10%, 20% and 25%.
Multiply the remaining fractions: 0.9 × 0.8 × 0.75 = 0.54. The buyer pays 54% of the MP, so the single discount is 46%. Adding 10 + 20 + 25 = 55% is the trap.
Answer: 46%
EXAMATLAS LEVEL
Q. On the same marked price, the difference between a single discount of 35% and two successive discounts of 20% and 15% is ₹360. Find the marked price and the selling price under the successive discounts.
Successive 20% and 15% = 20 + 15 − 3 = 32%. The difference from 35% is 3% of MP = ₹360, so MP = ₹12,000. SP under the successive discounts = 12,000 × 0.8 × 0.85 = ₹8,160.
Answer: MP ₹12,000; SP ₹8,160
Pattern 3: Buy x get y free, with or without an extra discount
[PYQ: NTPC UG CBT-1 21-Aug-2025 Shift-1 | NTPC Graduate CBT-1 27-Mar-2026 Shift-1]
EXAM LEVEL
Q. A shop offers "buy 4 get 1 free". Find the effective discount percent.
The customer gets 5 articles and pays for 4. Discount = 1/5 × 100 = 20%.
Answer: 20%
EXAMATLAS LEVEL
Q. A shop offers "buy 3 get 2 free" and then a further 10% off the bill. Find the effective discount. If the shopkeeper still earns an 8% profit, by what percent is the marked price above the cost price?
Paying for 3 of 5 articles means paying 60% of MP; a further 10% off makes it 0.6 × 0.9 = 54%. Effective discount = 46%. Profit condition: 0.54 MP = 1.08 CP, so MP = 2 CP, that is 100% above cost.
Answer: 46%; 100% above CP
Pattern 4: Marked price needed for a target profit after discount
[PYQ: NTPC Graduate CBT-1 9-Jun-2025 Shift-1 | NTPC Graduate CBT-1 27-Mar-2026 Shift-1]
EXAM LEVEL
Q. An article costs ₹600. The shopkeeper wants a 25% profit after giving a 20% discount. What should the marked price be?
Required SP = 600 × 1.25 = ₹750. MP = 750 ÷ 0.8 = ₹937.50. Formula: MP = CP × 125/80.
Answer: ₹937.50
EXAMATLAS LEVEL
Q. A trader marks his goods so that even after a 12.5% discount he gains 5%. If the marked price is ₹2,400, find his cost price and markup percent.
SP = 2,400 × 0.875 = ₹2,100. CP = 2,100 ÷ 1.05 = ₹2,000. Markup = 400/2,000 × 100 = 20%. Check with MP/CP = 105/87.5 = 1.2.
Answer: CP ₹2,000; markup 20%
Pattern 5: Ratio of marked price to cost price
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. A shopkeeper allows a 10% discount and still makes a 20% profit. Find the ratio of the marked price to the cost price.
MP/CP = 120/90 = 4/3. Ratio 4 : 3.
Answer: 4 : 3
EXAMATLAS LEVEL
Q. An article marked at ₹3,000 is sold with a discount of ₹360, and the shopkeeper still earns a profit of ₹240. Find the markup percent.
SP = 3,000 − 360 = ₹2,640, so CP = 2,640 − 240 = ₹2,400. Markup = 600/2,400 × 100 = 25% (discount 12%, profit 10%). Using 600/3,000 = 20% puts markup on the wrong base.
Answer: 25%
Pattern 6: Additional discount after a given discount
[PYQ: NTPC UG CBT-1 16-Jun-2026 Shift-2]
EXAM LEVEL
Q. An article marked at ₹2,000 carries a 25% sale discount, but a customer pays only ₹1,350. What additional discount percent did he get?
After the 25% discount the price is ₹1,500. The extra reduction is 150 on 1,500, that is 10%. Measuring 650 on 2,000 (32.5%) gives the total discount, not the additional one.
Answer: 10%
EXAMATLAS LEVEL
Q. A shopkeeper marks an article 50% above cost. During a sale he gives a 20% discount and then an additional discount on the reduced price, and still makes a 14% profit. Find the additional discount.
1.5 × 0.8 × (1 − d) = 1.14, so 1.2(1 − d) = 1.14 and 1 − d = 0.95. The additional discount is 5%.
Answer: 5%
60-Second Revision
- Discount on MP, profit on CP; MP/CP = (100 + P)/(100 − D).
- Markup m and discount d: net profit = m − d − md/100.
- Successive discounts: d₁ + d₂ − d₁d₂/100; three or more: multiply what remains.
- Buy x get y free: y/(x + y) × 100; then apply any extra discount as a factor.
- Additional discount is measured on the already reduced price.
- A single discount equal to the sum always beats the same discounts given one after another.
Next Step: Profit, Loss and Discount done. Take the Profit-Loss and Discount questions in the ExamAtlas RRB NTPC 2026 mock tests next; discount questions came in nine separate verified shifts tagged on this page, so drill the factor method until it takes under 40 seconds.