IPMAT Profit Loss and Discount 2027 — Formulas, Tricks and 40 Practice Problems
Profit, Loss and Discount is one of the most frequently tested topics in IPMAT 2027 Quantitative Ability. Every IPMAT Indore and JIPMAT paper has 3–5 questions from this topic. Mastering the core formulas, percentage shortcuts, and special cases like successive discounts and equivalent single discounts can easily fetch you 12–15 marks. This complete guide covers everything from basic formulas to advanced JEE-level applications.
Core Formulas You Must Know
Basic Definitions
- Cost Price (CP): Price at which article is purchased
- Selling Price (SP): Price at which article is sold
- Marked Price (MP): Price listed/tagged on article (before discount)
- Profit: SP > CP → Profit = SP − CP
- Loss: SP < CP → Loss = CP − SP
Key Formulas
- Profit % = (Profit / CP) × 100
- Loss % = (Loss / CP) × 100
- SP = CP × (100 + Profit%) / 100
- SP = CP × (100 − Loss%) / 100
- CP = SP × 100 / (100 + Profit%)
- Discount = MP − SP
- Discount % = (Discount / MP) × 100
- SP = MP × (100 − Discount%) / 100
Important Shortcuts and Special Cases
| Situation | Formula / Result | Example |
|---|---|---|
| Two articles sold at same SP; one at x% profit, other at x% loss | Net result = Loss of x²/100 % | 20% profit + 20% loss → 4% net loss |
| Successive discounts of a% and b% | Single equivalent = a + b − ab/100 | 20% + 10% → 28% single discount |
| Trader gives m articles for price of n (m > n) | Loss % = (m−n)/m × 100 | 3 for price of 2 → 33.33% loss |
| Selling m articles at CP of n (m < n) | Profit % = (n−m)/m × 100 | Sell 12, gain SP of 4 → 50% profit |
| Selling at x% above/below CP | Use multiplier: (100±x)/100 | 37.5% profit → SP = CP × 1.375 |
Fraction-to-Percentage Conversions (Must Memorise)
| Fraction | % | Fraction | % |
|---|---|---|---|
| 1/2 | 50% | 1/8 | 12.5% |
| 1/3 | 33.33% | 1/9 | 11.11% |
| 1/4 | 25% | 1/11 | 9.09% |
| 1/5 | 20% | 1/12 | 8.33% |
| 1/6 | 16.67% | 3/8 | 37.5% |
| 1/7 | 14.28% | 2/3 | 66.67% |
Step-by-Step Solved Examples
Example 1: Finding SP from Profit%
A shopkeeper buys an article for ₹500 and sells at 20% profit. Find SP.
Solution: SP = 500 × (100+20)/100 = 500 × 120/100 = ₹600
Example 2: Finding MP when SP and Discount% are given
An item is sold at ₹840 after 16% discount. Find Marked Price.
Solution: SP = MP × (100−16)/100 → 840 = MP × 84/100 → MP = 840×100/84 = ₹1000
Example 3: Successive Discounts
Successive discounts of 20% and 10% on a ₹1000 article. Find final SP.
Solution: Equivalent single discount = 20 + 10 − (20×10)/100 = 28%
SP = 1000 × (100−28)/100 = ₹720
Verify: 1000 → 20% off = 800 → 10% off = 720 ✓
Example 4: Classic “Same SP, x% profit and loss”
Two articles sold at ₹1200 each — one at 20% profit, other at 20% loss. Net result?
Solution: Net Loss% = x²/100 = 400/100 = 4%
Total CP = 1200×100/120 + 1200×100/80 = 1000 + 1500 = ₹2500
Total SP = 2400; Loss = 100; Loss% = 100/2500 × 100 = 4% ✓
Example 5: Gain on selling m articles at CP of n
Shopkeeper sells 12 pens and gains SP of 4 pens. Find Profit%.
Solution: SP of 12 − CP of 12 = SP of 4 → SP of 8 = CP of 12
Profit% = SP of 4 / CP of 12 × 100 = (SP of 12 − CP of 12)/CP of 12 × 100
Let CP per pen = 1, SP of 12 = 12×CP/8 = 1.5 per pen → Profit = 0.5 → Profit% = 50%
10 Practice MCQs — Solve Now
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Frequently Asked Questions (FAQ)
- Q: What is the formula for successive discounts?
- Equivalent single discount = a + b − ab/100. For 20% and 10%: 20 + 10 − 2 = 28%. Always results in a discount smaller than simple addition.
- Q: How many Profit-Loss questions come in IPMAT Indore?
- IPMAT Indore QA (45 questions) typically has 3–5 questions from Profit, Loss and Discount. One of the most tested arithmetic chapters alongside Percentages and Interest.
- Q: Two articles sold at same SP, one at x% profit and other at x% loss — net result?
- Always a LOSS. Net Loss% = x²/100. For x = 20%: Net Loss = 4%. Classic trap question in IPMAT.
- Q: What is the difference between MP and SP?
- MP = Marked Price (listed/tagged price before discount). SP = Selling Price (actual price paid). SP = MP × (100 − Discount%)/100.
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