Profit, Loss and Discount Formulas for CAT 2026: Every Formula, Shortcut and 15 PYQs
A complete profit, loss and discount cheatsheet for CAT 2026. It maps the eight core CP, SP and MP formulas, breaks down the two recurring CAT traps (the marked price chain and successive discounts), shares the multiplier-method shortcuts, and works through 15 solved PYQs at CAT difficulty.
Profit, Loss and Discount Formulas for CAT 2026: Every Formula, Shortcut and 15 PYQs
Two ideas decide almost every profit and loss question in CAT, and both are exactly where aspirants lose marks. The first is the marked price chain, where cost price becomes marked price becomes selling price, and one missed step throws the whole answer. The second is successive discounts, where adding 20 percent and 10 percent to get 30 percent is wrong every time. Master these two, layer the handful of base profit loss formulas CAT keeps reusing, and this becomes one of the most reliable scoring topics in Quant. This cheatsheet gives you every formula, the two key shortcuts, and 15 solved PYQs.
The Core Profit, Loss and Discount Formula Map
Everything in this topic builds on a small set of relationships between cost price (CP), selling price (SP), marked price (MP), and the percentages that link them. Learn these as a single map rather than isolated formulas, because CAT questions almost always chain two or three of them together. Here is the complete reference you need.
| Quantity | Formula |
|---|---|
| Profit | SP minus CP (when SP is greater than CP) |
| Loss | CP minus SP (when CP is greater than SP) |
| Profit % | (Profit / CP) times 100 |
| Loss % | (Loss / CP) times 100 |
| SP from CP | CP times (100 + Profit%) / 100 |
| CP from SP | SP times 100 / (100 + Profit%) |
| Discount | MP minus SP |
| Discount % | (Discount / MP) times 100 |
Successive discounts a% then b% = a + b - (a x b)/100
SP = CP x (1 + markup%) x (1 - discount%)
The single most important rule in this entire topic is that profit percent and loss percent are calculated on cost price, not selling price, unless a question explicitly says otherwise. Half of all profit and loss CAT 2026 errors trace back to using the wrong base. Burn that into memory before anything else.
The Marked Price Chain: The First CAT Trap
Layered questions describe a shopkeeper who marks goods above cost, then offers a discount, and asks for the final profit. The reliable method is to follow the chain in strict order: start at CP, apply the markup to get MP, apply the discount to get SP, then compare SP with CP for the profit or loss. Skipping straight from markup to profit is where aspirants go wrong.
CP = 100, marked 40% above cost, then 25% discount
MP = 100 x 1.40 = 140
SP = 140 x 0.75 = 105 → Profit = 5, Profit% = 5%
Notice that a generous-looking 40 percent markup with a 25 percent discount nets only a 5 percent profit. The discount applies to the larger marked price, so it eats more than its headline number suggests. Working the chain in order makes this obvious; guessing does not. This single discipline solves the majority of layered profit and loss questions you will meet in CAT.
Successive Discounts: The Second CAT Trap
When a question stacks two discounts, you cannot add them. A 20 percent discount followed by a 10 percent discount is not a 30 percent discount. The second discount applies to the already-reduced price, so the true reduction is smaller. The formula a + b - (a times b)/100 gives the exact net discount every time.
Discounts of 20% then 10%
Net = 20 + 10 - (20 x 10)/100 = 30 - 2 = 28%
So SP = MP x 0.72, not MP x 0.70
For three discounts, apply the two-discount formula to the first pair, then combine the result with the third. The multiplier method is even faster: just multiply the surviving fractions, so 20 percent then 10 percent becomes 0.80 times 0.90, which equals 0.72, the same 28 percent net discount. This is one of the cleanest discount tricks CAT rewards, and it scales to any number of discounts.
Adding discounts directly is the most common mistake on this topic. If you ever find yourself writing 20 + 10 = 30 percent for stacked discounts, stop. Use the multiplier method instead: multiply the surviving fractions and subtract from one. It is faster than the formula and removes the temptation to add. Drill it on the CAT practice question bank until the multiplier feels automatic.
Practise Profit and Loss with Real PYQs
Lock in the marked price chain and successive discount shortcut with targeted, CAT-level questions.
Drill Profit and Loss QuestionsShortcuts That Save Time in CAT
Beyond the two core traps, a few shortcuts turn slow profit and loss problems into ten-second solves. These appear constantly, so internalise them rather than re-deriving each time. Each one removes a calculation step under exam pressure.
- Multiplier method: Replace every percentage with a multiplier. A 25 percent profit is times 1.25; a 20 percent discount is times 0.80. Chain them in one line.
- Profit on SP versus CP: If profit is 25 percent of CP, it is 25/125 = 20 percent of SP. Convert bases instantly using profit/(100 + profit).
- Equal profit and loss on same price: Selling two items at the same price, one at x percent profit and one at x percent loss, always gives a net loss of (x/10) percent squared. A 20-20 split gives a 4 percent loss.
- False weight gain: A trader who sells at cost but gives w grams for 1000 grams gains (1000 - w)/w times 100 percent.
When a question gives only percentages and no actual rupee values, assume CP equals 100. Every markup, discount, and profit then becomes a clean number you can compute mentally. Plug back to the real base only at the end if the question asks for an amount. Pairing this with the speed methods in our speed math for CAT 2026 guide makes most of these questions a sub-minute solve.
15 Solved Profit, Loss and Discount PYQs for CAT 2026
These 15 questions mirror the difficulty and phrasing of actual CAT arithmetic. Try each before reading the answer, and apply the multiplier method wherever you can. Together they cover the marked price chain, successive discounts, base conversions, and the classic false-weight and equal-price traps.
Q1. An article costs 400 and sells for 500. Find the profit percent.
Profit = 100, Profit% = 100/400 x 100 = 25%.
Q2. An item sells for 720 at a 20% profit. Find the cost price.
CP = 720 / 1.20 = 600.
Q3. Goods marked 25% above cost are sold at a 10% discount. Find the profit percent.
CP 100 → MP 125 → SP 125 x 0.90 = 112.5 → Profit% = 12.5%.
Q4. Find the single discount equal to two successive discounts of 20% and 10%.
20 + 10 - (20 x 10)/100 = 28%.
Q5. An article sold at 270 gives a 10% loss. Find the cost price.
CP = 270 / 0.90 = 300.
Q6. Two items sell at 240 each, one at 20% profit and one at 20% loss. Net result?
CP1 = 200, CP2 = 300, total CP 500, total SP 480 → 4% net loss.
Q7. Marked 40% above cost, sold at 25% discount. Find profit percent.
CP 100 → MP 140 → SP 105 → Profit% = 5%.
Q8. If profit is 25% of cost price, what percent is it of selling price?
25 / 125 x 100 = 20%.
Q9. Selling at 90 gives a 10% loss. What selling price gives a 20% gain?
CP = 90 / 0.90 = 100 → SP = 100 x 1.20 = 120.
Q10. Find the net discount for three successive discounts of 10%, 10%, 10%.
100 x 0.90 x 0.90 x 0.90 = 72.9 → net discount 27.1%.
Q11. A trader sells at cost price but gives 900 g for 1 kg. Find the profit percent.
(100 / 900) x 100 = 11.11%.
Q12. The cost of 12 articles equals the selling price of 10 articles. Find profit percent.
(12 - 10) / 10 x 100 = 20%.
Q13. A 20% discount gives a selling price of 480. Find the marked price.
MP = 480 / 0.80 = 600.
Q14. An article gives 20% profit. If the selling price is doubled, find the new profit percent.
CP 100 → SP 120 → doubled SP 240 → profit 140 → 140%.
Q15. What markup over cost lets a 10% discount still yield a 17% profit?
Need SP = 117 after 10% discount → MP = 117 / 0.90 = 130 → 30% markup.
Score yourself out of 15. If you cleared 12 or more using the multiplier method, your profit and loss formulas are exam-ready. Below 9, redo the marked price chain and successive discount sections, then return. To see how a stronger arithmetic score moves your overall percentile, run the numbers through the CAT score predictor, and keep your wider CAT preparation balanced across the other arithmetic topics.
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