Quick Concept Summary
Discount problems are a staple in TNPSC and placement aptitude tests. The core relationships:
Key terms:
| Term | Full Form | Meaning |
|---|---|---|
| MP | Marked Price / MRP | Price printed on the product |
| CP | Cost Price | What the shopkeeper paid |
| SP | Selling Price | Actual price paid by buyer |
| Discount | — | Amount reduced from MP |
The golden rule: Discount is ALWAYS calculated on MP, never on CP.
Key Formulas
| Situation | Formula |
|---|---|
| Find Discount amount | Discount = MP − SP |
| Find Discount% | Discount% = (Discount / MP) × 100 |
| Find SP from MP and d% | SP = MP × (1 − d/100) |
| Find MP from SP and d% | MP = SP × 100 / (100 − d) |
| Two successive discounts d1, d2 | Net SP = MP × (1−d1/100) × (1−d2/100) |
| Effective single discount equivalent | d1 + d2 − (d1 × d2)/100 |
| Profit after discount (need CP) | Profit% = (SP − CP)/CP × 100 |
Worked Examples
Example 1 — Find SP from MP and discount%
Q: A shirt has a marked price of ₹500. A discount of 20% is offered. What is the selling price?
SP = MP × (1 − d/100) = 500 × (1 − 20/100) = 500 × 80/100 = ₹400
Example 2 — Find Discount%
Q: A book is marked at ₹250 and sold for ₹200. What is the discount percentage?
Discount = MP − SP = 250 − 200 = ₹50
Discount% = (50/250) × 100 = 20%
Example 3 — Find Marked Price
Q: After a 25% discount, a jacket is sold for ₹1500. What was its marked price?
MP = SP × 100 / (100 − d) = 1500 × 100 / (100 − 25) = 1500 × 100/75 = ₹2000
Example 4 — Successive Discounts
Q: A store offers two successive discounts of 30% and 20% on a television marked at ₹15,000. Find the final selling price.
After 1st discount (30%): SP₁ = 15000 × (1 − 30/100) = 15000 × 0.7 = ₹10,500
After 2nd discount (20%): SP₂ = 10500 × (1 − 20/100) = 10500 × 0.8 = ₹8,400
Effective discount check: 30 + 20 − (30×20)/100 = 50 − 6 = 44% SP = 15000 × (1 − 44/100) = 15000 × 0.56 = ₹8,400 ✓
Example 5 — Profit despite Discount
Q: A shopkeeper marks an article 40% above its cost price of ₹500 and then allows a 20% discount. Find his profit or loss percentage.
MP = 500 × (1 + 40/100) = 500 × 1.4 = ₹700
SP = 700 × (1 − 20/100) = 700 × 0.8 = ₹560
Profit = SP − CP = 560 − 500 = ₹60
Profit% = (60/500) × 100 = 12%
Example 6 — Finding Original Price from Final Price
Q: After successive discounts of 10% and 5%, a cycle costs ₹8,550. Find the marked price.
Let MP = x
SP = x × (1 − 10/100) × (1 − 5/100) = x × 0.9 × 0.95 = 0.855x
0.855x = 8550
x = 8550 / 0.855 = ₹10,000
Shortcuts and Tricks
Trick 1: Successive discounts ≠ sum of discounts
Two discounts of 20% and 20% appear to give 40%, but actually give: 20 + 20 − (20×20)/100 = 40 − 4 = 36% effective discount.
Always use the formula; never just add them.
Trick 2: Which is better — 40% off or 20% then 25% off?
Single 40%: effective = 40%
Successive 20%+25%: 20 + 25 − (20×25)/100 = 45 − 5 = 40%
They're exactly equal here. But this isn't always the case — always calculate.
Trick 3: If MP is x% above CP
SP = CP × (1 + x/100) × (1 − d/100)
Profit if SP > CP; Loss if SP < CP.
Trick 4: Quick SP calculation
| Discount | Multiply MP by |
|---|---|
| 10% | 0.9 |
| 20% | 0.8 |
| 25% | 0.75 |
| 30% | 0.7 |
| 50% | 0.5 |
TNPSC / Placement Exam Pattern
TNPSC: 1–2 questions per exam from Discount, usually combined with Profit and Loss. Typical patterns: find SP from MP and d%, or find profit% after a discount on marked price above CP.
Placement exams: May involve comparing two successive discount schemes, or finding original price from final price after discounts.
Common question types: 1. Find SP / MP / Discount% given two of the three 2. Successive discount — find effective discount or final price 3. Shopkeeper marks up X%, gives Y% discount — find net profit/loss 4. Two discount schemes — which is better?
Practice Questions
| # | Question | Answer |
|---|---|---|
| 1 | MP = ₹800, discount = 15%. Find SP. | ₹680 |
| 2 | MP = ₹600, SP = ₹480. Find discount%. | 20% |
| 3 | SP = ₹720 after 10% discount. Find MP. | ₹800 |
| 4 | Successive discounts 25% and 20% on ₹2000. Find SP. | ₹1200 |
| 5 | Two successive discounts of 10% and 10%. Find effective discount%. | 19% |
| 6 | MP = ₹1200, CP = ₹900, discount = 25%. Find profit or loss%. | Loss 11.1% |
| 7 | MP is 50% above CP of ₹400. Discount = 20%. Find SP and profit%. | SP=₹480, Profit=20% |
| 8 | Which is better: single 35% or successive 20% and 20%? | Single 35% (vs 36%) |
| 9 | After 30% discount, SP = ₹2100. Find MP. | ₹3000 |
| 10 | CP = ₹500. MP = 60% above CP. Discount = 25%. Find profit%. | 20% |