Profit and loss is among the most consistently tested topics across every major competitive examination in India. SSC CGL, RRB NTPC, IBPS PO, UPSC CSAT, and school board papers all include it — often in multiple questions per paper. The topic also forms the numerical backbone of real-world financial literacy, making it doubly worth mastering.
The challenge with profit and loss is not conceptual difficulty — most students understand what profit means. The challenge is the sheer variety of problem types: markup and discount, successive discounts, false weights, dishonest dealers, combined profit-loss, and equivalent single discount. Each type has a direct shortcut formula that bypasses multi-step algebra entirely.
This guide presents 10 of the most powerful shortcut formulas for profit and loss — one per problem type — with complete worked examples and the reasoning behind each formula so you understand not just how to apply it, but why it works.
The Core Vocabulary — Defined Once, Used Always
Before formulas, ensure these definitions are crystal clear:
- Cost Price (CP): The price at which an item is purchased
- Selling Price (SP): The price at which an item is sold
- Marked Price (MP): The price printed on the item (also called List Price)
- Profit: SP − CP (when SP > CP)
- Loss: CP − SP (when CP > SP)
- Discount: MP − SP (reduction from marked price)
- Overhead: Additional costs beyond purchase price (transport, storage, etc.)
Shortcut Formula 1: Basic Profit and Loss Percentage
Formulas:
- Profit% = (Profit / CP) × 100 = (SP − CP) / CP × 100
- Loss% = (Loss / CP) × 100 = (CP − SP) / CP × 100
Key point: Profit and loss percentage is ALWAYS calculated on Cost Price — never on Selling Price unless the question specifically states otherwise.
Worked Example 1:
A book bought for ₹240 sold for ₹300. Profit%?
- Profit = 300−240 = 60
- Profit% = (60/240) × 100 = 25%
Worked Example 2:
A phone bought for ₹8,000 sold for ₹6,400. Loss%?
- Loss = 8000−6400 = 1600
- Loss% = (1600/8000) × 100 = 20%
Worked Example 3:
An item sold for ₹1,170 at 30% profit. Find CP.
- CP = SP × 100/(100 + P%) = 1170 × 100/130 = ₹900
Shortcut Formula 2: Finding SP from CP and Profit/Loss %
Formulas:
- SP (profit) = CP × (100 + P%) / 100
- SP (loss) = CP × (100 − L%) / 100
Use these as single multipliers — never expand them step by step.
Worked Example 1:
CP = ₹450, Profit = 20%. Find SP.
- SP = 450 × 120/100 = 450 × 1.2 = ₹540
Worked Example 2:
CP = ₹1,200, Loss = 15%. Find SP.
- SP = 1200 × 85/100 = 1200 × 0.85 = ₹1,020
Worked Example 3:
CP = ₹750, Profit = 33.33%. Find SP.
- 33.33% = 1/3 → SP = 750 × 4/3 = ₹1,000
Shortcut Formula 3: Finding CP from SP and Profit/Loss %
Formulas:
- CP = SP × 100 / (100 + P%) — when profit is given
- CP = SP × 100 / (100 − L%) — when loss is given
Worked Example 1:
SP = ₹1,344, Profit = 12%. Find CP.
- CP = 1344 × 100/112 = 1344 × 25/28 = ₹1,200
Worked Example 2:
SP = ₹680, Loss = 15%. Find CP.
- CP = 680 × 100/85 = 680 × 20/17 = ₹800
Worked Example 3:
An article sold at 25% profit for ₹875. Find CP.
- CP = 875 × 100/125 = 875 × 4/5 = ₹700
Shortcut Formula 4: Markup and Discount Combined
When an item is marked up by M% and then discounted by D%, the net profit or loss is:
Net % = M − D − (M × D)/100
Positive result = profit, Negative result = loss.
Worked Example 1:
MP is 40% above CP. Discount = 25%. Net profit/loss%?
- Net = 40 − 25 − (40×25)/100 = 15 − 10 = +5% profit
Worked Example 2:
Marked up 30%, discounted 30%. Net?
- Net = 30 − 30 − (30×30)/100 = 0 − 9 = −9% loss
Worked Example 3:
A shopkeeper marks goods 50% above CP and allows 20% discount. Profit%?
- Net = 50 − 20 − (50×20)/100 = 30 − 10 = +20% profit
Worked Example 4:
After 10% discount SP = ₹1,620 and profit = 20%. Find MP.
- First find CP: CP = 1620×100/120 = ₹1,350
- SP = MP × 90/100 = 1620 → MP = 1620×100/90 = ₹1,800
Shortcut Formula 5: Successive Discounts
When two discounts D₁% and D₂% are applied one after another, the equivalent single discount is:
Equivalent Discount = D₁ + D₂ − (D₁ × D₂)/100
This is the same net formula — just applied to discounts instead of markup-discount.
Worked Example 1:
Two successive discounts of 20% and 10%. Equivalent single discount?
- = 20 + 10 − (20×10)/100 = 30 − 2 = 28%
Worked Example 2:
Successive discounts of 30% and 20%. Equivalent?
- = 30 + 20 − (30×20)/100 = 50 − 6 = 44%
Worked Example 3:
MP = ₹5,000. Successive discounts 25% and 16%. Final SP?
- Equivalent discount = 25+16−(25×16)/100 = 41−4 = 37%
- SP = 5000 × 63/100 = ₹3,150
Alternative method (often faster):
Apply discounts sequentially:
- After 25%: 5000×75/100 = 3750
- After 16%: 3750×84/100 = ₹3,150 ✓
Shortcut Formula 6: False Weight Shortcut
A dishonest dealer claims to sell at cost price but uses a false weight. The profit percentage is:
Profit% = (True weight − False weight) / False weight × 100
Worked Example 1:
A dealer uses 900g weight instead of 1kg. Profit%?
- = (1000 − 900)/900 × 100 = 100/900 × 100 = 11.11%
Worked Example 2:
A dealer uses 800g instead of 1kg AND sells at 10% profit. Total profit%?
- Profit from false weight = (1000−800)/800 × 100 = 25%
- Combined with 10% selling profit:
- Net = 25 + 10 + (25×10)/100 = 35 + 2.5 = 37.5%
Worked Example 3:
A shopkeeper claims 20% profit but uses 800g weight for 1kg. Actual profit%?
- Price for 800g at claimed 20% profit on 1kg CP:
- SP for 800g = 1kg's CP × 120/100
- Actual CP of 800g = 0.8 × CP of 1kg
- Actual Profit% = (SP − actual CP)/actual CP × 100
- = (1.2 − 0.8)/0.8 × 100 = 0.4/0.8 × 100 = 50%
Shortcut Formula 7: Two Items Same SP, One Profit One Loss
When two articles are sold at the same selling price, one at X% profit and one at X% loss, the net result is ALWAYS a loss:
Net Loss% = X² / 100
Worked Example 1:
Two items each sold at ₹1,200 — one at 20% profit, one at 20% loss. Net?
- Loss% = 20²/100 = 400/100 = 4% loss
Worked Example 2:
Two items each sold at ₹4,500 — one at 15% profit, one at 15% loss. Net result?
- Loss% = 15²/100 = 225/100 = 2.25% loss
Why always a loss? The CP of the loss item is higher than the CP of the profit item (since both have the same SP). The higher CP of the loss item pulls the combined result into net loss territory.
Shortcut Formula 8: Profit When Cost Price Is Unclear (CP1 + CP2 Problems)
When a person buys two quantities at different rates and sells the combined lot at one rate:
Combined CP = (Q₁ × R₁ + Q₂ × R₂) / (Q₁ + Q₂)
Then compare with selling rate to find profit/loss.
Worked Example:
A merchant buys 30 kg at ₹40/kg and 20 kg at ₹50/kg. Sells all at ₹48/kg. Profit or loss?
- Total CP = 30×40 + 20×50 = 1200 + 1000 = ₹2,200
- Total SP = 50 × 48 = ₹2,400
- Profit = 2400 − 2200 = ₹200
- Profit% = 200/2200 × 100 = 9.09%
Shortcut Formula 9: Overhead Costs
When additional costs beyond the purchase price are involved:
Effective CP = Purchase Price + Overhead Costs
Calculate profit/loss on effective CP, not purchase price alone.
Worked Example 1:
A bicycle bought for ₹3,200. ₹400 spent on repairs. Sold at ₹4,200. Profit%?
- Effective CP = 3200 + 400 = ₹3,600
- Profit = 4200 − 3600 = ₹600
- Profit% = 600/3600 × 100 = 16.67%
Worked Example 2:
A trader buys 100 items at ₹50 each. Pays ₹500 transport. Sells each at ₹58. Profit%?
- Total CP = 100×50 + 500 = ₹5,500
- Total SP = 100×58 = ₹5,800
- Profit% = 300/5500 × 100 = 5.45%
Shortcut Formula 10: Break-Even and Target SP
Given a desired profit%, find the minimum SP required:
Target SP = CP × (100 + Desired Profit%) / 100
Given a maximum acceptable loss%, find the minimum SP:
Minimum SP = CP × (100 − Max Loss%) / 100
Worked Example 1:
CP = ₹2,400. Minimum SP for 15% profit?
- SP = 2400 × 115/100 = ₹2,760
Worked Example 2:
CP = ₹5,000. Can afford maximum 8% loss. Minimum SP?
- SP = 5000 × 92/100 = ₹4,600
Worked Example 3:
A shopkeeper buys 120 items, 20 are damaged and unsellable. He wants 25% overall profit. At what price must he sell each good item?
- Total CP = 120 × CP (let CP per item = ₹x → total = 120x)
- Sellable items = 100
- Required total SP = 120x × 125/100 = 150x
- SP per item = 150x/100 = 1.5x → 50% above individual CP
All 10 Formulas — Quick Reference
| # | Situation | Formula |
|---|---|---|
| 1 | Basic Profit% | (SP−CP)/CP × 100 |
| 2 | SP from CP + Profit% | CP × (100+P%)/100 |
| 3 | CP from SP + Profit% | SP × 100/(100+P%) |
| 4 | Markup + Discount net | M − D − MD/100 |
| 5 | Successive discounts | D₁ + D₂ − D₁D₂/100 |
| 6 | False weight profit | (True−False)/False × 100 |
| 7 | Same SP, equal % profit+loss | Net loss = X²/100 |
| 8 | Mixed purchase, single SP | Combined CP vs combined SP |
| 9 | Overhead included | Effective CP = Purchase + Overhead |
| 10 | Target SP | CP × (100 ± %)/100 |
Common Mistakes and How to Avoid Them
| Mistake | Wrong | Correct |
|---|---|---|
| Calculating profit% on SP | Profit% = (SP−CP)/SP × 100 | Always on CP |
| Treating equal % profit+loss as break even | 20% profit + 20% loss = 0 | Always a loss of X²/100 |
| Adding successive discounts directly | 20%+10% = 30% discount | Equivalent = 28% only |
| Ignoring overhead in CP | Using purchase price directly | Add all costs to get effective CP |
| Using MP instead of CP for profit% | Profit on MP | Profit always on CP |