Discount Problems
Key Concepts
| # | Concept | Explanation |
|---|---|---|
| 1 | Marked Price (MP) | Price printed on the tag; 100 % base for discount calculations. |
| 2 | Discount % | (Discount ÷ MP) × 100; always calculated on MP, never on CP. |
| 3 | Selling Price (SP) | MP – Discount; or SP = MP × (100 – D%) / 100. |
| 4 | Successive Discounts | Two discounts D1% & D2% → single equivalent discount = D1 + D2 – (D1×D2)/100. |
| 5 | False Discount / Bogus Discount | MP is artificially raised first; actual discount on inflated MP → still profit. |
| 6 | Discount vs Profit | Discount is reduction on MP; Profit is gain over Cost Price (CP). |
| 7 | Cash Discount | Extra concession for immediate cash payment; applied after all discounts. |
| 8 | GST on Discounted Price | GST is calculated on SP after discount, not on MP. |
15 Practice MCQs
1. A shirt marked at ₹800 is sold at 15 % discount. Find SP.
**Options:** A) ₹680 B) ₹720 C) ₹650 D) ₹750Answer: A) ₹680
Solution: SP = 800 × (100 – 15)/100 = 800 × 0.85 = 680.
Shortcut: 10 % = 80, 5 % = 40 → 15 % = 120 → 800 – 120 = 680.
Tag: Basic Discount
2. After 20 % discount, SP is ₹560. Find MP.
**Options:** A) ₹700 B) ₹672 C) ₹750 D) ₹650Answer: A) ₹700
Solution: MP = 560 × 100 / 80 = 700.
Shortcut: 80 % ≡ 560 → 1 % ≡ 7 → 100 % ≡ 700.
Tag: MP from SP
3. Single equivalent discount for 25 % and 10 % successive discounts is
**Options:** A) 32.5 % B) 35 % C) 30 % D) 27.5 %Answer: A) 32.5 %
Solution: 25 + 10 – (25×10)/100 = 35 – 2.5 = 32.5 %.
Shortcut: Use formula D1 + D2 – D1D2/100.
Tag: Successive Discount
4. A trader marks up goods 40 % above CP and then gives 20 % discount. Find profit %.
**Options:** A) 12 % B) 20 % C) 8 % D) 10 %Answer: A) 12 %
Solution: Let CP = 100 → MP = 140 → SP = 140 × 0.8 = 112 → Profit 12 %.
Shortcut: 1.4 × 0.8 = 1.12 → 12 % profit.
Tag: Mark-up & Discount
5. The discount on a ₹1,200 jacket is ₹240. Discount % is
**Options:** A) 20 % B) 25 % C) 16.67 % D) 15 %Answer: A) 20 %
Solution: (240/1200) × 100 = 20 %.
Tag: Discount %
6. MP = ₹900, Discount = 2 successive discounts of 20 % and 10 %. Find SP.
**Options:** A) ₹648 B) ₹630 C) ₹720 D) ₹600Answer: A) ₹648
Solution: 900 × 0.8 × 0.9 = 648.
Shortcut: 0.8 × 0.9 = 0.72 → 900 × 0.72 = 648.
Tag: Successive Discount
7. A watch bought for ₹500 is labelled ₹800. What is the maximum discount % so that no loss occurs?
**Options:** A) 37.5 % B) 40 % C) 25 % D) 20 %Answer: A) 37.5 %
Solution: Max discount = 800 – 500 = 300 → 300/800 = 37.5 %.
Tag: Break-even Discount
8. A shopkeeper gives 10 % discount on MP and still gains 20 %. If MP is ₹600, find CP.
**Options:** A) ₹450 B) ₹480 C) ₹500 D) ₹440Answer: A) ₹450
Solution: SP = 600 × 0.9 = 540; CP = 540/1.2 = 450.
Shortcut: 540 ÷ 6 × 5 = 450.
Tag: CP from MP & Gain
9. Single discount equivalent to three successive discounts 10 %, 20 %, 25 % is
**Options:** A) 46 % B) 50 % C) 54 % D) 48 %Answer: A) 46 %
Solution: 0.9 × 0.8 × 0.75 = 0.54 → discount = 46 %.
Tag: Triple Successive
10. A sofa listed at ₹15,000 is sold for ₹12,750. Find discount %.
**Options:** A) 12 % B) 15 % C) 17.5 % D) 20 %Answer: B) 15 %
Solution: (2250/15000) × 100 = 15 %.
Tag: Basic Discount
11. If a discount of 30 % is given, the profit is 5 %. What will be the profit % if discount is 15 %?
**Options:** A) 25 % B) 27.5 % C) 30 % D) 32.5 %Answer: B) 27.5 %
Solution: Let CP = 100; 30 % discount → SP = 0.7 MP = 105 → MP = 150. New SP = 150 × 0.85 = 127.5 → Profit 27.5 %.
Tag: Variable Discount
12. A dealer marks goods 50 % above CP and allows 20 % discount. What is the profit %?
**Options:** A) 30 % B) 25 % C) 20 % D) 15 %Answer: C) 20 %
Solution: 1.5 × 0.8 = 1.2 → 20 % profit.
Tag: Mark-up & Discount
13. Two shops offer (a) single 40 % discount, (b) successive 20 % + 25 % discounts. Which is better for customer?
**Options:** A) Same B) (a) better by 5 % C) (b) better by 5 % D) (b) better by 10 %Answer: B) (a) better by 5 %
Solution: (b) equiv. = 20 + 25 – 5 = 40 %, but 0.8 × 0.75 = 0.6 → 40 % discount same; actually 40 % single is better because 0.6 vs 0.6 → same; but on ₹100 both give 60, so Same → Correct choice A.
Tag: Compare Discounts
14. A phone MP ₹20,000 is sold at 12 % discount, then additional 5 % cash discount. Find net price.
**Options:** A) ₹16,720 B) ₹16,800 C) ₹17,000 D) ₹16,600Answer: A) ₹16,720
Solution: 20000 × 0.88 × 0.95 = 16720.
Shortcut: 0.88 × 0.95 = 0.836 → 20000 × 0.836 = 16720.
Tag: Cash Discount
15. A retailer offers “Buy 3 get 1 free”. Effective discount % is
**Options:** A) 20 % B) 25 % C) 33.33 % D) 30 %Answer: B) 25 %
Solution: Pay for 3, get 4 → discount = 1/4 = 25 %.
Tag: BOGO Discount
Speed Tricks
| Situation | Shortcut | Example |
|---|---|---|
| Two successive discounts D1, D2 | Use (D1+D2–D1D2/100) once | 20 % + 30 % → 44 % |
| Mark-up x % then discount y % | Net change = x – y – xy/100 | 40 % up, 20 % off → 12 % gain |
| MP & SP given, need Discount % | Discount % = (MP – SP)/MP × 100 | MP 1000, SP 850 → 15 % |
| CP, desired gain x %, discount y % | MP = CP × (100+x)/(100–y) | CP 500, gain 20 %, discount 20 % → MP = 500×120/80 = 750 |
| Triple successive discounts | Multiply decimals once | 0.9×0.8×0.75 = 0.54 → 46 % discount |
Quick Revision
| Point | Detail |
|---|---|
| 1 | Discount is always calculated on MP, never on CP. |
| 2 | SP = MP × (100 – D%) / 100. |
| 3 | Two successive discounts: combine via D1 + D2 – (D1D2)/100. |
| 4 | Mark-up & discount: net profit = (1+m)(1–d) – 1. |
| 5 | Break-even discount % = (MP – CP)/MP × 100. |
| 6 | Cash discount is applied after trade discount. |
| 7 | BOGO “Buy 2 get 1” → 33.33 % effective discount. |
| 8 | GST is computed on SP after all discounts. |
| 9 | For same discount %, single discount better than successive. |
| 10 | Memorise fraction twins: 12.5 % = 1/8, 37.5 % = 3/8, 62.5 % = 5/8. |
BETA
