Master the Fraction Method - Solve CP, SP, Markup & Discount Problems Without Formulas! Trusted by 50,000+ IBPS, SBI, SSC aspirants!
Profit and Loss is the backbone of banking arithmetic. It appears in almost every competitive exam — IBPS PO, SBI Clerk, SSC CGL, Railway and more. Understanding the relationship between Cost Price (CP), Selling Price (SP), and Marked Price (MP) is essential!
In IBPS PO 2023, 5-7 questions came from Profit, Loss, Discount & Markup. The Fraction Method helped toppers avoid decimal calculations entirely! That's 2-3 minutes saved on just this topic!
| Term | Definition |
|---|---|
| Cost Price (CP) | The price at which an item is purchased. This is your investment. |
| Selling Price (SP) | The price at which an item is sold. This is your return. |
| Marked Price (MP) | The price labeled on the product (before any discount). |
| Profit | When SP > CP. Formula: Profit = SP - CP |
| Loss | When CP > SP. Formula: Loss = CP - SP |
| Discount | Reduction from MP. Formula: Discount = MP - SP |
Remember: Profit% and Loss% are always calculated on Cost Price, not on Selling Price. This is the most common mistake students make!
Formulas are good for school, but in exams, use the Fraction Method to avoid decimal calculations entirely!
20% Profit = 1/5. Here, denominator (5) = CP units, numerator (1) = Profit units.
For Profit: SP = CP + Profit = 5 + 1 = 6 units
For Loss: SP = CP - Loss = 5 - 1 = 4 units
Given value (SP or CP) = X units. Find what 1 unit equals.
Required value = Required units × Value of 1 unit. Done!
Question: A shopkeeper sells an item for ₹630 at 12.5% Profit. Find CP.
Solution using Fraction Method:
• 12.5% = 1/8
• CP = 8 units, Profit = 1 unit
• SP = 8 + 1 = 9 units
• Given: SP = ₹630 = 9 units
• 1 unit = 630/9 = ₹70
• CP = 8 units = 8 × 70 = ₹560
✅ Answer: CP = ₹560
Question: An item bought for ₹400 is sold at 25% loss. Find SP.
Solution:
• 25% = 1/4
• CP = 4 units, Loss = 1 unit
• SP = 4 - 1 = 3 units
• Given: CP = ₹400 = 4 units
• 1 unit = 400/4 = ₹100
• SP = 3 units = 3 × 100 = ₹300
✅ Answer: SP = ₹300
If two articles are sold at the same selling price, one at x% profit and other at x% loss:
Question: Two articles sold at ₹500 each. One at 20% profit, one at 20% loss. Find net result.
Solution:
• Loss % = (20/10)² = 2² = 4% Loss
✅ Answer: 4% Net Loss (regardless of SP value!)
If a shopkeeper marks up by x% and also cheats on weight by y%:
Question: A shopkeeper claims to sell at cost price but uses 900g weight instead of 1kg. Find gain%.
Solution:
• Markup = 0% (selling at CP), Weight cheat = 10% (100g less)
• Gain = (0 + 10) / (100 - 10) × 100
• Gain = 10/90 × 100 = 11.11%
✅ Answer: 11.11% Profit
When multiple discounts are given one after another:
Question: Find equivalent discount for 20% and 10% successive discounts.
Solution:
• Equivalent = 20 + 10 - (20×10/100)
• Equivalent = 30 - 2 = 28%
✅ Answer: 28% Equivalent Discount
Must-know fractions:
10% = 1/10, 12.5% = 1/8, 16.67% = 1/6, 20% = 1/5, 25% = 1/4, 33.33% = 1/3, 50% = 1/2
Never calculate profit/loss percentage on SP! The base is always Cost Price.
Discount percentage is calculated on Marked Price, not on CP or SP.
CP → (1 + Markup%) → MP → (1 - Discount%) → SP → Compare with CP for Profit/Loss
Profit-Loss becomes intuitive after consistent practice. Aim for 30 questions for 5 days!
P% = (P/CP) × 100
L% = (L/CP) × 100
D% = (D/MP) × 100
Loss = (x/10)²%
Ab aapko Profit & Loss ki poori samajh aa gayi! Time to test your skills with real exam-level questions!
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