Profit Loss and Discount Formulas for CAT 2026: 22 + 15 PYQs
Profit loss formulas for CAT 2026 are the second-highest contributor in CAT Arithmetic after percentages, and the two topics share an underlying layer. CAT 2026 will give you 2 to 3 direct profit-loss questions and 1 to 2 adjacent problems that ride on the markup-discount chain or false-weight logic. This cheatsheet pins 22 shortcuts across four recognition blocks, then closes with 15 tricky CAT-level questions that mirror the trap patterns setters reuse year after year.
The reason CAT profit-loss questions trap so many aspirants is that the topic looks straightforward in school textbooks but is engineered on multiplier logic at the CAT level. A 40% markup with a 25% discount is not a 15% profit. A 20% successive discount on a 10% successive discount is not 30%. The 22 shortcuts below are organised around those trap patterns so each formula maps to a recognition cue.
Why CAT Tests Profit and Loss Through Multipliers, Not Subtraction
Every CAT-level question that draws on the profit loss formulas for CAT 2026 is, underneath, a chain of multipliers acting on a cost price base. A markup is a multiplier of (1 plus markup%). A discount is a multiplier of (1 minus discount%). A successive discount is a product of two such multipliers. A false weight is a multiplier of true-over-false. Once aspirants see the entire topic through this multiplier lens, the trap answers fall away and solutions compress to a single line. The 22-formula cheatsheet is structured to install this lens.
The split between school-level and CAT-level profit-loss content is exactly here. School textbooks teach subtraction-first: SP minus CP equals profit. That works on direct questions but breaks the moment a chain appears. CAT 2026 questions almost always involve chains, which is why this blog leads with the chain identities and treats subtraction as the entry block.
The 22 Profit Loss and Discount Formulas for CAT 2026
The cheatsheet groups all 22 profit loss formulas for CAT 2026 into four blocks. Each block has a recognition cue describing the question type that triggers it. Working block by block embeds the multiplier-first habit that the drill depends on.
Block 1 — CP, SP, MP and Basic Profit Loss (6 formulas)
The basic block is the entry point. These six identities define cost price, selling price, marked price, profit, loss, and the percentage forms. Recognition cue: a single transaction without chains, where one of CP, SP, profit%, or loss% is unknown.
| # | Formula | Use case |
|---|---|---|
| 1 | Profit = SP − CP; Loss = CP − SP | Direct rupee profit or loss. |
| 2 | Profit% = (Profit / CP) × 100 | Profit percentage from rupee values. |
| 3 | Loss% = (Loss / CP) × 100 | Loss percentage from rupee values. |
| 4 | SP = CP × (100 + Profit%) / 100 | Selling price for a target profit. |
| 5 | SP = CP × (100 − Loss%) / 100 | Selling price for a known loss. |
| 6 | CP = SP × 100 / (100 ± Profit% or Loss%) | Reverse-finding cost price. |
Block 2 — Markup and Discount Chain (6 formulas)
The markup-discount block is where CAT profit-loss questions earn most of their reputation. A marked price is set above cost, then a discount is offered on the marked price. The chain is CP into MP via markup, then MP into SP via discount. Recognition cue: a question that mentions marked price, list price, sticker price, or discount on a stated reference.
| # | Formula | Recognition cue |
|---|---|---|
| 7 | MP = CP × (1 + Markup% / 100) | Set marked price from cost. |
| 8 | Discount = MP − SP; Discount% = (Discount / MP) × 100 | Discount value and percentage. |
| 9 | SP = MP × (1 − Discount% / 100) | Selling price after one discount. |
| 10 | SP = CP × (1 + Markup) × (1 − Discount) | Full markup-discount chain. |
| 11 | Net Profit% = ((1 + Markup) × (1 − Discount) − 1) × 100 | Profit percentage from chain multipliers. |
| 12 | For zero profit: Markup% = (Discount / (100 − Discount)) × 100 | Break-even markup setting. |
Block 3 — Successive Discounts and Chains (5 formulas)
The successive block extends the chain logic to multiple discounts on the same item. CAT setters embed two- and three-step discount chains in nearly every recent paper. Recognition cue: two or more discounts mentioned with words like then, further, an additional, or in succession.
| # | Formula | Use case |
|---|---|---|
| 13 | Net % after −a% then −b% = a + b − (ab / 100) | Two successive discounts. |
| 14 | Net multiplier for chain of discounts = (1 − d1) × (1 − d2) × (1 − d3)… | Three or more discounts. |
| 15 | Two equal successive discounts of x% = 2x − (x2 / 100) | Equal-rate chain shortcut. |
| 16 | Equivalent single discount for −a% then −b% then −c% = 1 − (1−a)(1−b)(1−c) all over 1, expressed as percentage | Three-step single-discount conversion. |
| 17 | Discount + cashback chain: SP = MP × (1 − d) × (1 − c) | Discount stacked with cashback or coupon. |
Block 4 — False Weights, Mixtures and Special Cases (5 formulas)
The special-cases block covers false-weight problems, two-item average profit, and partial-loss recovery. CAT recycles these patterns in 1 of every 3 papers, usually as a stand-alone Arithmetic question. Recognition cue: dishonest trader, false weight, sells two items at the same price, or recovers cost on remaining stock.
| # | Formula / Rule | Use case |
|---|---|---|
| 18 | False weight gain% = ((True − False) / False) × 100 | Dishonest trader using false weight. |
| 19 | Two items at same SP, one at +x% one at −x%: net loss% = x2 / 100 | Equal-SP opposite-percentage trap. |
| 20 | Average profit% on two items = ((SP1 + SP2) − (CP1 + CP2)) / (CP1 + CP2) × 100 | Composite profit on two transactions. |
| 21 | Recover cost on remaining: SP of fraction f at profit% = (CP / f) × (1 + total target profit / 100) | Partial-stock loss-recovery problem. |
| 22 | Combined dishonest trader (markup + false weight): net% = ((1 + markup) × (True / False)) − 1, as percentage | Compound dishonesty pattern. |
Three Profit Loss Traps That Recur in CAT Papers
Three traps recur across the profit loss formulas for CAT 2026 question set, even though each of the underlying identities is straightforward. The first is direct addition of successive discounts. Two 20% discounts is not a 40% discount. The correct net is 20 + 20 minus (400 / 100) = 36%. The trap option at 40% catches aspirants who forget the third term. The second trap is the equal-SP opposite-percentage pattern. Selling two items at the same SP, one at 20% profit and one at 20% loss, is not a break-even. Formula 19 gives a net loss of x squared over 100, which is 4% in this case. The intuition that gains and losses cancel is the trap.
The third trap is the false-weight base error. When a dishonest trader uses a 900-gram weight in place of 1000 grams, the gain percentage is calculated on the false weight given (900), not on the true claim (1000). The correct gain is (100 / 900) times 100 = 11.11%, not 10%. CAT sets the trap option at 10% to catch the wrong-base computation.
15 Tricky Profit Loss and Discount PYQs for CAT 2026
These 15 questions cover all four blocks of the cheatsheet. Each is tagged with the block and the formula it tests. Drill them under timed conditions, target under 90 seconds per question, and use the cheatsheet only for recall after attempting.
A pen bought for 80 is sold for 100. Find profit percentage.
Profit = 20. Profit% = (20 / 80) × 100 = 25%. Answer: 25%
A book is bought for 240 and sold at 15% profit. Find SP.
SP = 240 × 1.15 = 276. Answer: 276
An item sold for 540 at a 10% loss. Find its cost price.
CP = 540 / 0.90 = 600. Answer: 600
Cost 200, marked up 50%, sold at 20% discount. Find profit percentage.
SP = 200 × 1.5 × 0.8 = 240. Profit = 40. Profit% = 20%. Answer: 20%
A trader offers a 25% discount and wants to make no profit and no loss. What markup percentage must he set?
Markup = (25 / 75) × 100 = 33.33%. Answer: 33.33%
A shopkeeper wants a 12% profit after offering a 10% discount. By what percent must he mark up cost?
(1 + markup) × 0.9 = 1.12. Markup = (1.12 / 0.9) − 1 = 0.2444 = 24.44%. Answer: 24.44%
An item is marked at 1000 and offered at 20% then 10% discount. Find final price.
1000 × 0.8 × 0.9 = 720. Answer: 720
Find the single discount equivalent to 20% then 10%.
Net multiplier = 0.8 × 0.9 = 0.72. Equivalent discount = 28%. Answer: 28%
An item with MP 500 is sold after 10%, 20%, and 5% successive discounts. Find SP.
500 × 0.9 × 0.8 × 0.95 = 342. Answer: 342
A 1200 phone gets a 25% discount and an additional 10% cashback on the discounted price. Final amount paid?
1200 × 0.75 × 0.9 = 810. Answer: 810
A trader uses an 800-gram weight in place of 1 kg while selling at cost. Find his gain percentage.
Gain% = (1000 − 800) / 800 × 100 = 25%. Answer: 25%
Two items are sold at 600 each. One at 20% profit and the other at 20% loss. Find net loss percentage.
Apply formula 19: net loss% = 202 / 100 = 4%. Answer: 4% loss
A trader loses 25% of his stock. At what profit percentage must he sell the remaining 75% to break even?
SP of remaining = CP of full stock. So 0.75 × CP × (1 + p) = CP, giving (1 + p) = 4/3, p = 33.33%. Answer: 33.33%
A wholesaler sells to a retailer at 20% profit, who then sells to a customer at 10% profit. If the customer pays 660, what was the wholesaler's cost?
CP × 1.2 × 1.1 = 660. CP × 1.32 = 660. CP = 500. Answer: 500
A shopkeeper marks up goods by 20% and uses a 900-gram weight in place of 1 kg. Find his net gain percentage.
Net multiplier = 1.20 × (1000 / 900) = 1.333. Net gain = 33.33%. Answer: 33.33%
Chain Profit Loss Into Your CAT 2026 Arithmetic Block
Profit Loss sits one step downstream of Percentages, which means the multiplier reflex compounds the moment percentages are locked in. A diagnostic-driven plan sequences these two topics back to back in weeks one and two so the cluster compounds.
Chain My Arithmetic Multiplier BlockWhere Profit Loss Sits in the CAT 2026 Arithmetic Cluster
Profit Loss is the second topic in the CAT Arithmetic sequence: Percentages first, then Profit Loss, then SI CI, then Ratio, then Time Speed Distance, then Time and Work. The dependency is mechanical, since markup and discount are percentage operations on a cost base. Aspirants who try to learn profit-loss before percentages always end up looping back to the percentages cheatsheet. A focused 4 to 5 day study block, scheduled in week two of any 9-month CAT plan, covers the topic.
For a working professional with limited weekly hours, this 4 to 5 day block can stretch to 8 to 10 days, which still places the topic comfortably in month one. The Optima Learn CAT exam guide sequences the rest of the Arithmetic cluster, and the CAT 2026 waitlist details page explains how the diagnostic-driven planner decides which Arithmetic topics each aspirant needs to prioritise.
Three Reflexes That Compress Profit Loss Solves to Under 60 Seconds
Once 22 formulas are memorised, three reflexes separate aspirants who finish profit-loss questions in 60 seconds from those who take three minutes. Reflex one: multiplier-first. Convert every percentage in the question into a multiplier before solving. Markup 25% becomes 1.25. Discount 20% becomes 0.80. False weight 900 of 1000 becomes 10/9. Reflex two: chain-then-compute. List all multipliers in one line, multiply, then read the answer. Avoid intermediate rupee values until the final step. Reflex three: equal-SP trap check. Whenever two items are sold at the same SP with opposite percentages, immediately suspect formula 19. These three install through timed drill, and the CAT preparation blogs library has companion cheatsheets on Percentages, SI CI, and Quadratic Equations.
Common Doubts About Profit Loss Preparation for CAT 2026
Are profit-loss and percentages really the same topic?
The underlying logic is the same: a multiplier acting on a base. The recognition cues differ. Percentages questions mention rates, salaries, populations, marks, or votes. Profit-loss questions mention CP, SP, MP, markup, discount, or trader. Drilling both sets of recognition cues together compounds the cluster faster than studying them in isolation.
Should I memorise the markup-for-zero-profit formula?
Yes. Formula 12 turns up in 30% of CAT discount questions, and aspirants who do not know it spend a minute setting up an equation that the formula solves in one line. The exact form: required markup% equals (discount / (100 minus discount)) times 100. Memorise it cold.
How tricky are the recent CAT 2024 and CAT 2025 profit and loss CAT 2026 PYQs?
Recent papers lean heavily on chain multipliers, false weights, and multi-trader sequences. Two of the three questions in CAT 2024 and one of two in CAT 2025 used a chain of at least three multipliers. The drill is to never solve a profit-loss question with intermediate rupee values; build the multiplier chain first.
How do I revise this topic one week before CAT 2026?
A one-week revision plan: day one, re-read the 22-formula cheatsheet. Day two, drill the markup-discount chain. Day three, drill successive discounts. Day four, drill false-weight and equal-SP trap patterns. Day five, attempt 15 mixed-block PYQs under timed conditions. Day six, review every error and re-attempt. Day seven, scan the cheatsheet for 15 minutes only before the exam.
Final note. Profit loss formulas CAT 2026 reduce to 22 shortcuts across four blocks, with the markup-discount chain and successive-discount blocks carrying the most weight. The topic rewards multiplier thinking over subtraction thinking. Drill block by block, build the three reflexes, and the CAT score predictor alongside mocks will track the lift across Profit Loss, SI CI, and Mixtures downstream.
