Profit and Loss Formulas for CAT 2026: Every Formula + 15 PYQs
Every profit and loss formula CAT 2026 aspirants need, with the successive-discount equivalence shortcut, marked-price vs cost-price decoding logic, and 15 CAT previous year questions solved using fraction multipliers. Covers the 9 core formulas, the false-weight pattern, the equal-SP loss trap, and the four repeatable CAT P&L question patterns.
Profit and Loss Formulas for CAT 2026: Every Formula + 15 PYQs
Profit and loss is the most-tested arithmetic topic on CAT — and the one CAT aspirants most often get wrong with the right formula. The reason is structural: the topic looks like a percentage problem on the surface but tests a chain of four quantities (cost price, marked price, selling price, profit) that need to stay aligned through every operation. Aspirants who memorise the formulas in isolation lose marks the moment a question stacks two operations. Aspirants who memorise the chain solve in 30 seconds.
This guide covers every profit and loss formula for CAT 2026, the successive discount equivalence shortcut, the marked-price-vs-cost-price decoding logic, the false-weight pattern, and 15 CAT previous year questions solved using the multipliers rather than long-form arithmetic.
Profit and loss runs on a four-quantity chain: CP → (markup) → MP → (discount) → SP. Memorise 9 formulas: profit/loss percent, SP-from-CP, successive discount equivalence (D1 + D2 − D1·D2/100), markup, false-weight, and the dishonest-dealer multiplier. The 30-second shortcut: convert every percent to a fraction (20% = 6/5, 25% = 5/4) and chain fractions. CAT 2020 to CAT 2024 averaged 2 to 3 P&L questions per cycle worth 6 to 9 marks. The 15 PYQs below cover every tested pattern.
The Four-Quantity Price Chain
Every CAT profit and loss problem moves money along the same four-quantity chain. Aspirants who internalise the chain answer faster because they always know which quantity is the input and which is the output. The chain is the single most important diagram in this topic.
Profit or loss is the gap between Step 1 (CP) and Step 3 (SP). The markup and discount happen at different stages and must not be combined directly.
The Nine Core Profit and Loss Formulas (Memorise These)
The formulas below cover every variant CAT has tested in the last decade. Memorise the structure first, then commit one example per formula to mental cache. When the mock test arrives, the pattern recognition is faster than the algebra.
Profit, loss, and their percentages
Profit = SP − CP · Loss = CP − SPProfit % = (Profit / CP) × 100
Loss % = (Loss / CP) × 100
Always over cost price — never selling price. The most common CAT trap is dividing the profit by SP instead of CP.
Selling price multiplier
SP = CP × (1 + Profit% / 100)SP = CP × (1 − Loss% / 100)
Convert profit percent to a fraction multiplier. 20 percent profit = 6/5, 25 percent = 5/4, 50 percent = 3/2. Multiply CP by the fraction.
Reverse calculation
CP = SP / (1 + Profit% / 100)CP = SP / (1 − Loss% / 100)
Inverse of Formula 2. CAT questions that give SP and ask CP need this multiplier in the denominator. Use fraction form to avoid decimals.
Discount on the marked price
SP = MP × (1 − Discount% / 100)MP = CP × (1 + Markup% / 100)
Markup happens on cost price. Discount happens on marked price. Different bases. Aspirants who use the same base for both lose marks.
The most-tested CAT shortcut for stacked discounts
D_equivalent = D1 + D2 − (D1 × D2) / 100Two successive 20% discounts give an equivalent single discount of 36%, not 40%. CAT routinely tests this because aspirants who add discounts produce wrong answers in under 20 seconds. The same identity extends to three discounts: apply the formula twice.
Combined markup and discount on cost price
Net Profit % = Markup% − Discount% − (Markup% × Discount%) / 100This is Formula 5 with one sign flipped. The markup adds, the discount subtracts, and the cross-term subtracts further. The classic CAT case: 40 percent markup followed by 25 percent discount produces only 5 percent net profit, not 15 percent.
Dishonest shopkeeper using a wrong weight
Profit % = (Error / True Weight − Error) × 100Or: Profit % = (Claimed Weight / Actual Delivered − 1) × 100
If the shopkeeper claims 1 kg but delivers 900 g, profit is 100/900 × 100 = 11.11 percent. CAT often combines false-weight with a markup — chain the two using Formula 6's logic.
The cost-price-of-articles equivalence
If CP of x articles = SP of y articlesProfit % = ((x − y) / y) × 100
If the cost price of 11 articles equals the selling price of 10 articles, the profit is 1/10 × 100 = 10 percent. Common CAT pattern that confuses aspirants who set up the equation wrong.
The classic CAT loss trap
If two items sold at same SP, one at +x% profit and one at −x% loss:Net loss % = x² / 100
Selling one item at 20% profit and another at 20% loss for the same SP produces an overall 4 percent loss, not break-even. CAT exploits this counterintuitive identity. Memorise the x squared over 100 form.
Aspirants apply percentages to the wrong base. Markup is on CP. Discount is on MP. Profit and loss percent are on CP. Mixing the bases produces wrong answers that look right. Before computing, draw the chain (Step 1 to Step 2 to Step 3) and label the base for every percent.
For every CAT-style percent, convert to the fraction form before computing. SP at 25 percent profit on CP of 1200 = 1200 × 5/4 = 1500. Faster than 1200 × 1.25 in mental arithmetic.
For loss multipliers, flip the relation: 20 percent loss = 4/5. 25 percent loss = 3/4. CAT problems with a 20 percent profit followed by 25 percent discount chain to 6/5 × 3/4 = 18/20 = 9/10, that is, net 10 percent loss.
The Fraction Multiplier Quick-Reference Table
For CAT-style percentages, the fraction multipliers below let aspirants solve every profit-loss-discount problem in mental arithmetic. Drill these until they are automatic; the time savings compound across the 2 to 3 P&L questions per paper.
| Percent | Profit multiplier (+x%) | Loss multiplier (−x%) | Fraction form (best) |
|---|---|---|---|
| 10 % | 1.10 or 11/10 | 0.90 or 9/10 | 11/10 (+) · 9/10 (−) |
| 12.5 % | 1.125 or 9/8 | 0.875 or 7/8 | 9/8 (+) · 7/8 (−) |
| 16.67 % | 1.1667 or 7/6 | 0.8333 or 5/6 | 7/6 (+) · 5/6 (−) |
| 20 % | 1.20 or 6/5 | 0.80 or 4/5 | 6/5 (+) · 4/5 (−) |
| 25 % | 1.25 or 5/4 | 0.75 or 3/4 | 5/4 (+) · 3/4 (−) |
| 33.33 % | 1.3333 or 4/3 | 0.6667 or 2/3 | 4/3 (+) · 2/3 (−) |
| 50 % | 1.50 or 3/2 | 0.50 or 1/2 | 3/2 (+) · 1/2 (−) |
When a CAT P&L problem chains multiple operations, convert every percent into a fraction, chain the fractions, and only convert back at the end. The cumulative multiplier of 20 percent profit then 10 percent discount is 6/5 × 9/10 = 54/50 = 27/25 = 1.08 — an 8 percent net profit. The chain answers in 15 seconds; the decimal version takes 45.
How Profit and Loss Connects to Other CAT Topics
Profit and loss lives in the percentage-applications cluster alongside simple interest, compound interest, and ratio and proportion. The skill that transfers is the multiplier — the same fraction logic that solves a 20 percent markup also solves a 20 percent compound interest rate. The simple interest and compound interest formulas for CAT 2026 guide covers the successive-period compounding identity, which is mathematically the same as Formula 5 here.
The ratio and proportion formulas guide covers the partnership and investment-sharing patterns that often combine with profit-loss problems. CAT 2024 specifically tested a hybrid question that required Formula 9 (equal-SP loss) plus a partnership-ratio split — the topic crossover is intentional.
Want a personalised CAT 2026 arithmetic plan with daily P&L drills and a paced PYQ track?
Build My CAT Arithmetic Plan15 CAT PYQs on Profit and Loss
The 15 questions below cover every profit-loss pattern CAT has tested. Each solution uses the fraction multiplier or the shortcut identity, not the long-form decimal arithmetic.
Basic Profit Percent
A trader buys an item for Rs. 400 and sells it for Rs. 500. Find the profit percent.
Successive Discount
Find the single equivalent discount for two successive discounts of 20 percent and 25 percent.
Markup then Discount
An article is marked 40 percent above CP. A 25 percent discount is given. Find the net profit percent.
Equal SP Trap
Two articles are sold at Rs. 1200 each. One yields a 20 percent profit and the other a 20 percent loss. Find the overall loss percent.
False Weight
A shopkeeper sells at cost price but uses a 900 g weight instead of 1 kg. Find the profit percent.
CP from SP at Loss
By selling an article at Rs. 720, a man loses 10 percent. Find the CP.
Articles Bought-vs-Sold Equivalence
If the CP of 12 articles equals the SP of 10 articles, find the profit percent.
Three Successive Discounts
Find the single discount equivalent to three successive discounts of 10 percent, 20 percent, and 25 percent.
Markup Required to Net 20 Percent Profit
If a discount of 10 percent is offered, what markup on CP gives a 20 percent profit?
SP from CP and Loss
An article whose CP is Rs. 800 is sold at a 12.5 percent loss. Find the SP.
Profit Percent from CP and SP
A shopkeeper buys 60 chocolates for Rs. 1800 and sells them at Rs. 35 each. Find the profit percent.
Discount and Profit Combined
A shopkeeper marks the price at 20 percent above cost and gives a 10 percent discount on the marked price. Find the profit percent.
Loss to Profit Swap
A man sells an article at a 10 percent loss. If he had sold it for Rs. 100 more, he would have made a 10 percent profit. Find the CP.
Dishonest Dealer Profit
A dishonest dealer sells at cost price but cheats by 10 percent on weight. Find his profit percent.
Bulk Profit on N Items
A trader buys 100 articles for Rs. 6000 and sells 80 articles at Rs. 75 each. The rest are unsold. Find his overall profit or loss percent.
The Four Patterns CAT Keeps Testing
The 15 questions above collapse into four repeatable CAT patterns. Spend the first 8 seconds of every P&L question deciding which pattern applies, then solve.
- Pattern A — Single percent computation. One CP, one SP, find the percent. Apply Formula 1 directly.
- Pattern B — Stacked operations. Markup-then-discount or discount-then-discount. Chain fraction multipliers (Formulas 5 and 6).
- Pattern C — Equal-SP or articles-equivalence trap. Two items with equal SP and opposite percents. Apply Formula 9 directly.
- Pattern D — False weight or dishonest dealer. Apply Formula 7 with the claimed-versus-delivered ratio.
For aspirants whose P&L accuracy is below 70 percent in mocks despite knowing the formulas, the gap is almost always in pattern recognition. The fix: drill 40 mixed P&L questions across the four patterns, tagging each one by pattern before solving. By Day 5, the pattern recognition fires in under 8 seconds. The CAT 2026 marking scheme guide covers the +3/−1/0 marking math that makes a 30-second P&L attempt one of the highest-ROI questions on the paper, and the CAT exam overview page shows where P&L sits in the broader Quant section.
- Memorise 9 formulas: profit/loss percent, SP-from-CP, markup-then-discount, false weight, equal-SP trap.
- Draw the four-quantity chain (CP → MP → SP) before computing anything.
- Markup is on CP. Discount is on MP. Profit and loss percent are on CP. Never mix bases.
- Convert every percent into a fraction multiplier before chaining (20% = 6/5, 25% = 5/4, 12.5% = 9/8).
- For successive discounts, apply D1 + D2 − D1·D2/100 — never add discounts directly.
- Equal-SP profit-loss trap: overall loss = x²/100 percent, not break-even.
- False weight profit = error / (true weight − error) × 100.
- Spot Pattern A (single), B (stacked), C (equal-SP/articles), or D (false weight) in under 8 seconds.
Profit and loss is not a percent problem. It is a chain problem with percent operations. Draw the chain. Chain the fractions. Show up.
Get a Personalised CAT 2026 Arithmetic Plan
The Optima Learn CAT 2026 waitlist builds a paced arithmetic track with daily P&L drills, pattern-tagged PYQs, and post-mock analysis on every cycle.
Build My CAT Arithmetic Plan
Optima Learn Editorial Team
CAT preparation specialists publishing structured guides on the CAT exam, IIM admissions, and MBA entrance prep. We track CAT Quant formula frequency, pattern-mapping shortcuts, and PYQ-to-mock conversion ratios across cycles.
Drill these Quant concepts on real PYQs
20,000+ tagged CAT Quant PYQs, sorted by difficulty and topic.