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Every CAT Set Theory formula on one page — Venn diagrams, De Morgan's laws, cardinality formulas, and set identities — each with a worked example.
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Profit & Loss
CAT'26 QUANT CHEATSHEET
Every profit & loss formula and CAT shortcut you need for CAT 2026 — on one page.
Profit & Loss questions on CAT rarely stop at a single sale — they chain markups into discounts, stack successive price changes, or hide the profit inside a false-weight scam. The whole topic runs on one habit: assume a convenient CP (usually ₹100) and convert every percentage into a multiplier before combining anything. This sheet lays out every formula you need for the CAT quant section: profit and loss basics, the SP and CP formulas, the pre-computed multiplier table, successive profit/loss and discounts, markup versus discount, false weights, and the no-profit-no-loss recovery shortcut, each with a worked example in real numbers. Keep it open while you practise, and after a mock check where you stand on the CAT score predictor to see which idea is costing you marks.
Dev note: the canonical route
/cheatsheets/optima-learn-profit-loss-cheatsheet is not live yet
(no /cheatsheets hub in the current sitemap). Built production-ready as a drop-in once it ships.Profit & Loss: every formula you need
1Core Idea
Whether you gain or lose depends only on SP versus CP.
Profit = SP − CP | Loss = CP − SP
Example: SP > CP means profit; SP < CP means loss.
CAT Hack: Assume CP = ₹100 whenever a question is purely about percentages — it makes every number a direct percent.
2Profit %
Profit expressed as a percentage, always of the cost price.
Profit % = ((SP − CP) ÷ CP) × 100
Example: CP=₹500, SP=₹600, profit=₹100 → (100/500)×100 = 20%.
3Loss %
Loss expressed as a percentage, also always of the cost price.
Loss % = ((CP − SP) ÷ CP) × 100
Example: CP=₹800, SP=₹680, loss=₹120 → (120/800)×100 = 15%.
Common Mistake: Profit % and Loss % are always calculated on CP, never on SP.
4Selling Price Formula
Scale the cost price up or down by the given percentage.
Profit: SP = CP×(1+x/100) | Loss: SP = CP×(1−x/100)
Example: 20% profit → SP=1.2·CP; 25% loss → SP=0.75·CP.
5Cost Price Formula
Work backward from the selling price to the cost price.
Profit: CP = SP÷(1+x/100) | Loss: CP = SP÷(1−x/100)
Example: SP=₹960 at 20% profit → CP = 960/1.2 = ₹800.
6Profit / Loss Fraction Table
The common percentages, pre-converted to multipliers.
| Profit | Multiplier | Loss | Multiplier |
|---|---|---|---|
| 10% | 11/10 | 10% | 9/10 |
| 20% | 6/5 | 20% | 4/5 |
| 25% | 5/4 | 25% | 3/4 |
| 50% | 3/2 | 50% | 1/2 |
Example: a 25% profit means SP = 5/4 of CP; a 25% loss means SP = 3/4 of CP.
CAT Hack: Memorise these multipliers so you can jump straight from CP to SP without recomputing 1±x/100 each time.
7Successive Profit & Loss
Combine two successive profits or losses into one net change.
Net Change = a + b + (ab ÷ 100)
Example: 20% profit then 10% profit → 20+10+(20·10)/100 = 32% net profit.
CAT Favourite: 20% + 20% is not 40% — the actual combined change here would be 44%, not a simple sum.
8Discount Basics
Discount is measured off the marked price, not the cost price.
Discount = MP − SP | Discount % = (Discount ÷ MP) × 100
Example: MP=₹1000, SP=₹850 → discount = ₹150 → 15% off the marked price.
Common Mistake: Discount % is always calculated on the marked price (MP), never on the cost price (CP).
9Successive Discounts
Two discounts applied one after another, combined into one.
Equivalent Discount = a + b − (ab ÷ 100)
Example: 20% then 10% discount → 20+10−(20·10)/100 = 28% equivalent single discount.
10Markup & Discount
A markup on CP followed by a discount off that marked price.
SP = CP × (1+Markup%/100) × (1−Discount%/100)
Example: 25% markup then 20% discount → 1.25·0.8 = 1.0 → no profit, no loss.
CAT Insight: Markup % is not the same as Profit % — a markup can be fully cancelled out by the discount that follows.
11False Weights
Selling short weight while charging for the full weight.
Profit % = (Error ÷ True Weight) × 100
Example: 1000g sold as if it were 900g (i.e. 100g short) → 100/900 × 100 = 11.11% profit.
Common Mistake: CAT loves false-weight questions — the profit comes from the shortfall over the reduced (true) weight, not the labelled weight.
12No Profit No Loss
The break-even condition, and the recovery percentage after a loss.
CP = SP (break-even) | after a loss of x%, recovery needed = x/(100−x) × 100
Example: after a 20% loss, recovery needed = 20/(100−20)×100 = 25% profit on the new price.
CAT exam shortcuts, traps & revision
13
CAT Exam Shortcuts
- Assume CP = ₹100 whenever percentages are involved
- Convert percentages into fractions before combining them
- Use multipliers (1±x/100) directly instead of recomputing each time
- Markup × Discount: multiply the two factors to find the net effect
- Successive discount: a+b−ab/100 (opposite sign to successive profit/loss)
- False weight: profit % = error ÷ true weight × 100
14
Most Common CAT Traps
- Calculating Profit % on SP instead of CP.
- Calculating Discount % on CP instead of MP.
- Adding successive discounts directly: 20% + 10% is not 30% (actual is 28%).
- Confusing Markup % with Profit % — they are not the same thing.
- Assuming equal profit and loss percentages cancel out (they don't).
15
30-Second Revision Box
- Profit = SP−CP; Loss = CP−SP
- SP = CP × multiplier; CP = SP ÷ multiplier
- Discount = MP−SP; Discount % is on MP
- Successive profit/loss: a+b+ab/100; successive discount: a+b−ab/100
- Markup × Discount can net to no profit, no loss
- False weight profit % = error ÷ true weight × 100
Profit & Loss rewards thinking in multipliers over raw percentage arithmetic — once a markup and a discount both become clean fractions, stacking them is one multiplication, not two separate calculations. Drill this sheet until the multiplier table and the successive-change formulas are reflex, then test them on full sets and track progress with the CAT score predictor. It pairs directly with the Percentages cheat sheet, since the successive-change logic is identical in both. For more guides, browse the Optima Learn blog or explore every study guide, work through the CAT exam hub, and when you want mentor-led prep, book a free CAT 2026 call.
