Quick Answer: Profit and loss questions in SSC and bank exams become 10-second problems with three core tricks: (1) treat successive discounts as multiplying factors (10% + 20% = 0.9 × 0.8 = 0.72, i.e., 28% net discount), (2) switch percentage bases between CP and SP using factors, and (3) assume a false cost price of ₹100 whenever only percentages are given. This guide covers all six exam-tested shortcuts with solved examples.
- Why Profit and Loss Questions Are Scoring in SSC & Bank Exams
- Percentage-Base Switching: The Fundamental Idea
- Shortcut 1: Successive Discount Chains (Discount-Price Chain Method)
- Shortcut 2: Profit and Loss as Multiplying Factors
- Shortcut 3: False Cost Price (Fake CP) Trick
- Shortcut 4: Marked Price, Discount and Profit Together
- Shortcut 5: Equal Profit-Loss on Two Items Sold at the Same Price
- Shortcut 6: Goods Left Free / Faulty Weight Problems
- Worked SSC & Bank Exam Examples (Step-by-Step)
- Common Mistakes Aspirants Make in Profit-Loss Questions
- Practice Set and Quick Revision Table
- Frequently Asked Questions
- Q: Can successive discounts be added directly, like 10% + 20% = 30%?
- Q: What is the multiplying factor method in profit and loss?
- Q: When should I assume CP = 100 in exam questions?
- Q: If two items are sold at the same price with x% profit and x% loss, is there overall no profit no loss?
- Q: How are faulty weight problems solved using base switching?
- Related reading
Why Profit and Loss Questions Are Scoring in SSC & Bank Exams
Profit and loss reliably contributes 2–4 questions in SSC CGL and CHSL Tier-1 and 1–2 questions in IBPS PO/Clerk and SBI prelims. The syllabus is small, the question patterns repeat every year, and once you internalise multiplying factors, most questions collapse into a single line of calculation. The patterns that dominate are:
- Successive discounts on a marked price (SSC CGL favourite)
- Marked price → discount → profit chains (IBPS PO standard)
- Dishonest shopkeeper / faulty weight problems (SSC CHSL)
- Two items sold at the same price with equal % profit and loss (both exams)
Percentage-Base Switching: The Fundamental Idea
Every profit-loss confusion in exams comes from one root cause: profit is calculated on CP, discount is calculated on MP. A 20% profit is not the same as a 20% discount reversed — the bases differ.
The clean fix is the multiplying factor:
- Profit of p% → SP = CP × (1 + p/100)
- Loss of p% → SP = CP × (1 − p/100)
- Discount of d% → SP = MP × (1 − d/100)
So a 20% profit means the factor is ×1.2; a 25% loss means ×0.75. Once you stop converting percentages back to rupees and start chaining factors, base-switching becomes automatic.
Shortcut 1: Successive Discount Chains (Discount-Price Chain Method)
Never add successive discounts. Multiply the surviving factors.
Example: Successive discounts of 10% and 20%.
Factor = 0.9 × 0.8 = 0.72 → SP is 72% of MP → net discount = 28%, not 30%.
Fast formula for two discounts: Net discount = a + b − ab/100 = 10 + 20 − 200/100 = 28%.
Example with numbers: MP = ₹500, discounts 10% and 20%.
Shortcut: 500 × 0.9 × 0.8 = ₹360. Done in one line.
Shortcut 2: Profit and Loss as Multiplying Factors
Convert every percentage into a factor and chain it along the price path:
SP = CP × (1 ± p/100)
Example: A shopkeeper sells at 20% profit; SP = ₹480. Find CP.
CP = 480 ÷ 1.2 = ₹400. No equations, no variables.
Chained example: CP → +25% → intermediate → −10% → final. Net factor = 1.25 × 0.9 = 1.125 → overall 12.5% profit.
Shortcut 3: False Cost Price (Fake CP) Trick
When a question gives only percentages and no absolute value, assume CP = 100 (or MP = 100 for discount-only questions). This kills all fractions.
Example: A trader marks goods 40% above CP and gives a 15% discount. Find profit %.
Shortcut: CP = 100 → MP = 140 → SP = 140 × 0.85 = 119 → profit = 19%.
Use false CP = 100 whenever the answer sought is a percentage, not a rupee amount. If actual rupee values are involved, combine the trick with one ratio step at the end.
Shortcut 4: Marked Price, Discount and Profit Together
The full chain in one equation:
CP × (1 + p/100) = MP × (1 − d/100)
Example: After allowing a 12% discount, a trader still makes 32% profit. Find MP above CP (SSC-style).
Let CP = 100. SP = 132. MP × 0.88 = 132 → MP = 150 → marked 50% above cost price.
This single-equation setup handles nearly every MP-discount-profit question in IBPS and SSC papers.
Shortcut 5: Equal Profit-Loss on Two Items Sold at the Same Price
If two items are sold at the same price, one at x% profit and the other at x% loss, the transaction is always a net loss, and the loss is:
Net loss % = (x/10)²
Example: Two phones sold at ₹9,900 each — one at 10% profit, one at 10% loss.
Shortcut: loss = (10/10)² = 1% loss.
Verification: CP₁ = 9900/1.1 = 9000; CP₂ = 9900/0.9 = 11000; total CP = 20000, total SP = 19800 → loss 200 = 1%. ✓
Shortcut 6: Goods Left Free / Faulty Weight Problems
Dishonest shopkeeper questions are pure base switching. If a trader claims to sell at CP but uses a false weight:
Gain % = (Error ÷ (True value − Error)) × 100
Example: A shopkeeper sells at CP but gives only 900 g per kg.
Gain = 100/(1000−900) × 100 = 100/900 × 100 = 11.11% gain.
Equivalent statement: “sells 10 articles for the CP of 11” — the factor is 11/10, so gain = 10%. Watch the wording: “10 free per 100” differs from “sells 11 for the price of 10”.
Worked SSC & Bank Exam Examples (Step-by-Step)
Example 1 (SSC CGL style): Successive discounts of 20% and 12.5%. Equivalent single discount?
- Normal: two separate rupee calculations, ~40 seconds.
- Shortcut: 0.8 × 0.875 = 0.70 → 30% single discount in 5 seconds.
Example 2 (IBPS PO style): MP = ₹12,000, two successive discounts of 10% each, find SP.
Shortcut: 12000 × 0.9 × 0.9 = ₹9,720 (not 12000 × 0.8 = 9600).
Example 3 (SSC CHSL style): CP of 15 articles = SP of 12 articles. Profit %?
Shortcut: profit factor = 15/12 = 1.25 → 25% profit.
Example 4: A trader marks 60% above CP and offers “Buy 4, get 1 free”. Profit %?
Shortcut: assume CP per article = 100, MP = 160. He sells 5 for the price of 4 → revenue = 4 × 160 = 640 on cost 5 × 100 = 500. Factor = 640/500 = 1.28 → 28% profit.
Common Mistakes Aspirants Make in Profit-Loss Questions
- Adding successive discounts: 10% + 20% ≠ 30%. Always multiply factors (0.72, i.e., 28%).
- Applying discount on CP: discount is always on MP; profit is always on CP.
- Assuming “equal profit and loss cancels out”: it never does — there is always a loss of (x/10)²%.
- Wrong base in faulty weights: gain % uses (true − error) as the denominator, not the claimed weight.
- Converting to rupees unnecessarily: stay in factors until the final step.
Practice Set and Quick Revision Table
| Concept | Shortcut Formula / Factor |
|---|---|
| Successive discounts a%, b% | Net = a + b − ab/100 |
| Profit p% | SP = CP × (1 + p/100) |
| Discount d% | SP = MP × (1 − d/100) |
| MP–discount–profit chain | CP(1 + p/100) = MP(1 − d/100) |
| Same SP, x% profit and x% loss | Net loss = (x/10)² % |
| Faulty weight | Gain % = error/(true − error) × 100 |
| CP of x articles = SP of y articles | Profit factor = x/y |
Practice Questions (answer hints in brackets):
- Successive discounts of 15% and 20% — net discount? (Hint: 0.85 × 0.8 = 0.68 → 32%)
- SP = ₹540 at a 10% loss. Find CP. (Hint: 540 ÷ 0.9 = ₹600)
- MP is 40% above CP; discount 25%. Profit or loss %? (Hint: 140 × 0.75 = 105 → 5% profit)
- Two cycles sold at ₹1,980 each, one at 10% profit, one at 10% loss. Net result? (Hint: (10/10)² = 1% loss)
- A trader gives 800 g per kg at CP. Gain %? (Hint: 200/800 × 100 = 25%)
Frequently Asked Questions
Q: Can successive discounts be added directly, like 10% + 20% = 30%?
No. Successive discounts multiply: 0.9 × 0.8 = 0.72, so the net discount is 28%, always less than the simple sum.
Q: What is the multiplying factor method in profit and loss?
Convert each percentage change to a factor (1 ± p/100) and multiply them along the price chain — e.g., CP × 1.2 × 0.9 gives the final SP after a 20% profit and a 10% reduction.
Q: When should I assume CP = 100 in exam questions?
Whenever only percentages are given and no absolute values are mentioned. It removes fractions and makes the entire calculation mental math.
Q: If two items are sold at the same price with x% profit and x% loss, is there overall no profit no loss?
No — there is always a net loss equal to (x/10)² percent, e.g., 20% profit and 20% loss gives a 4% net loss.
Q: How are faulty weight problems solved using base switching?
Compare the claimed weight base with the actual weight base using multiplying factors. Gain % = error ÷ (true value − error) × 100.
Related reading
- Simple vs Compound Interest Shortcuts: Ratio Trick and Difference Formula for SSC & Bank Exams
- Percentage Change Shortcuts: Base Switching and Successive Change Tricks for SSC & Bank Exams
Quick revision
- Successive discounts on a marked price (SSC CGL favourite)
- Marked price → discount → profit chains (IBPS PO standard)
- Dishonest shopkeeper / faulty weight problems (SSC CHSL)
- Two items sold at the same price with equal % profit and loss (both exams)
- Profit of p% → SP = CP × (1 + p/100)
- Loss of p% → SP = CP × (1 − p/100)
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