1. Basics
- Discount is always on the Marked Price (MP). SP = MP − discount.
- Profit/loss is on CP. Keep MP, SP and CP separate.
2. Formulas
| Case | Formula |
|---|---|
| Successive discounts a% and b% | Single equivalent = a + b − ab/100 |
| Three successive | Apply twice |
| Mark up m%, discount d% | Net % = m − d − md/100 (gain if +) |
| "Buy x get y free" | Discount % = y/(x + y) × 100 |
| MP from CP for a target gain after discount | MP = CP × (100 + g)/(100 − d) |
3. Solved examples
Successive discounts of 20% and 10% = 20 + 10 − 2 = 28%.
(ASO 2015) Marked 40% above CP, discount 25% → 140 × 0.75 = 105 → 5% gain.
Buy 4 get 1 free → 1/5 = 20% discount.
CP ₹600; wants 20% gain after giving 10% discount → MP = 600 × 120/90 = ₹800.
MP ₹1,500, SP ₹1,200 → discount 300/1500 = 20%.
Single discount equal to 10%, 20%, 25%: 10 + 20 − 2 = 28; then 28 + 25 − 7 = 46%.
Solved examples by question type
Each type that comes in the ASO paper, worked step by step. Try it yourself first, then read the solution.
Basic level
Example 1. A shirt is marked at ₹2,500 and sold at a 15% discount. Its selling price is:
(a) ₹2,175 (b) ₹375 (c) ₹2,350 (d) ₹2,125
Answer: (d) ₹2,125
Solution: SP = 2,500 × 85/100 = ₹2,125.
Example 2. A shirt is marked at ₹1,500 and sold at a 10% discount. Its selling price is:
(a) ₹1,486 (b) ₹1,350 (c) ₹1,400 (d) ₹150
Answer: (b) ₹1,350
Solution: SP = 1,500 × 90/100 = ₹1,350.
ASO exam level
Example 3. Two successive discounts of 20% and 10% are equal to a single discount of:
(a) 30% (b) 32% (c) 28% (d) 27%
Answer: (c) 28%
Solution: Single = a + b − ab/100 = 20 + 10 − 2 = 28%.
Example 4. A trader marks his goods 50% above cost price and allows a discount of 20%. His gain percent is:
(a) 20% (b) 23% (c) 10% (d) 30%
Answer: (a) 20%
Solution: Net = 50 − 20 − (50×20)/100 = 20%. Check: 100 → 150 → 120.
Example 5. A shopkeeper allows 10% discount and still gains 17%. By what percent above cost did he mark his goods?
(a) 27% (b) 35% (c) 25% (d) 30%
Answer: (d) 30%
Solution: MP × 90/100 = CP × 117/100 → MP = 130% of CP. Mark-up = 30%.
Example 6. The marked price of a lamp is ₹1,000. It is sold for ₹850. The rate of discount is:
(a) 12% (b) 15% (c) 17.65% (d) 17%
Answer: (b) 15%
Solution: Discount = 150. Rate = 150/1,000 × 100 = 15%. Discount is on MP.
Example 7. The marked price of a lamp is ₹800. It is sold for ₹640. The rate of discount is:
(a) 17% (b) 25% (c) 20% (d) 22%
Answer: (c) 20%
Solution: Discount = 160. Rate = 160/800 × 100 = 20%. Discount is on MP.
Example 8. A shop offers 'buy 4, get 1 free'. The effective discount percent is:
(a) 23% (b) 20% (c) 25% (d) 10%
Answer: (b) 20%
Solution: You pay for 4 and get 5. Discount = 1/5 × 100 = 20%.
Advanced level
Example 9. An article costs ₹1,200. At what price must it be marked so that after a 20% discount there is still a 20% profit?
(a) ₹1,440 (b) ₹1,680 (c) ₹1,850 (d) ₹1,800
Answer: (d) ₹1,800
Solution: SP = 1,200 × 120/100 = 1,440. MP = SP × 100/80 = ₹1,800.
Topic-wise practice for Discount (Quant): Successive discount, marked price above cost, discount with profit. Useful for OPSC ASO, OSSC, OSSSC and other Odisha exams.
Question types covered
- Marked price, discount and SP
- Successive discounts and their single equivalent
- Marked x% above cost and discount y%: profit or loss
- Discount with a profit target
- Buy x get y free offers