◆ QA · Arithmetic

Profit & Loss, formulas + CAT PYQs

An A-to-Z formula sheet, a graded confidence-building set, and real CAT previous-year questions, every answer independently solved and code-verified.

12formula blocks
15CAT PYQs
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Formula Sheet CAT PYQs

Formula & Concept Sheet (A → Z)

Core terms, every formula, the high-yield CAT results, and the traps.

1Core terms
  • CP cost price · SP selling price · MP marked price.
  • Profit = SP − CP; Loss = CP − SP.
  • All profit/loss % are on CP unless stated.
2Profit% / Loss%
  • Profit% = (SP−CP)/CP ×100; Loss% = (CP−SP)/CP ×100.
  • SP = CP(1 ± %/100); CP = SP/(1 ± %/100).
  • SP 850 @25% ⇒ CP = 850/1.25 = 680.
3Marked price & discount
  • Discount is on MP: Disc% = (MP−SP)/MP ×100.
  • SP = MP(1 − disc%/100). Chain: CP → markup → MP → discount → SP.
  • CP 500, +40%, −10% ⇒ SP = 630 (26% profit).
4Successive discounts
  • a% then b%: net = a + b − ab/100 (multiply factors).
  • 20% then 10% ⇒ 28% off (×0.8×0.9 = 0.72).
5Markup-then-discount
  • SP = CP(1 + markup%/100)(1 − disc%/100).
  • Equal markup & discount ⇒ a loss (×1.2×0.8 = 0.96 ⇒ −4%).
6Two articles, same SP
  • One at +x%, other at −x%, same SP ⇒ always a net loss = x²/100 %.
  • Both ±20% ⇒ 4% loss (no profit, no break-even).
7Profit on CP vs on SP
  • "m% of SP" ⇒ profit% on CP = m/(100−m) ×100.
  • Always check the base (CP, SP, or MP).
8Dishonest dealer
  • Sells at CP but short weight ⇒ gain% = error/(true − error) ×100.
  • 1000 g claimed, 900 g given ⇒ 100/900 = 11.11%.
9Chained transactions
  • Mfr → wholesaler → retailer: multiply factors (1.1×1.3×1.5).
  • Buy-back/resell chains ⇒ track net rupees = Σ(SP−CP).
10Mixtures & overall profit
  • Overall% = (total SP − total CP)/total CP ×100, use totals, not averages.
  • Parts + wastage ⇒ Σ part-SP = (1 + target%)·total CP.
11Equating two scenarios
  • Write SP − CP = profit for each scenario; subtract to cancel fixed costs.
  • Karim: add the two eqns ⇒ 0.25b = 20 ⇒ b = 80.
12Traps
  • Profit/loss % on CP; discount % on MP, don't mix bases.
  • Successive % are not additive, multiply factors.
  • "Same SP, ±x%" ⇒ instant loss x²/100 %.

Revision Set, 20 questions

Easy → moderate. Aim 100% on Level 1, 80%+ on Level 2, build speed on Level 3.

Level 1 · Warm-up basics

EasyB1
An article bought for Rs. 400 is sold for Rs. 500. Find the profit percent.
Show solution
25%  (100/400 × 100)
EasyB2
An article costing Rs. 800 is sold at 12.5% profit. Find the selling price.
Show solution
Rs. 900  (800 × 1.125)
EasyB3
An article is sold for Rs. 850 at a 25% profit. Find its cost price.
Show solution
Rs. 680  (850 / 1.25)
EasyB4
An article costing Rs. 1200 is sold at a 15% loss. Find the selling price.
Show solution
Rs. 1020  (1200 × 0.85)
EasyB5
An article is sold for Rs. 720 at a 10% loss. Find the cost price.
Show solution
Rs. 800  (720 / 0.90)
EasyB6
The marked price of an item is Rs. 1000 and a 20% discount is given. Find the selling price.
Show solution
Rs. 800  (1000 × 0.80)
EasyB7
An article with cost price Rs. 500 is marked 40% above cost and then sold at a 10% discount. Find the selling price and the profit percent.
Show solution
SP = Rs. 630, profit = 26%  (500 × 1.4 × 0.9 = 630)
EasyB8
Two successive discounts of 20% and 10% are given on a marked price of Rs. 500. Find the final price.
Show solution
Rs. 360  (500 × 0.8 × 0.9; net discount 28%)

Level 2 · Easy CAT applications

EasyCAT 2017E1
The manufacturer of a table sells it to a wholesale dealer at a profit of 10%. The wholesale dealer sells the table to a retailer at a profit of 30%. Finally, the retailer sells it to a customer at a profit of 50%. If the customer pays Rs. 4290 for the table, then its manufacturing cost (in Rs) is
  • (1) 1500
  • (2) 2000
  • (3) 2500
  • (4) 3000
Show solution
(2) 2000. 4290 = MC × 1.1 × 1.3 × 1.5 = MC × 2.145 ⇒ MC = 2000.
EasyCAT 2019E2
Mukesh purchased 10 bicycles in 2017, all at the same price. He sold six of these at a profit of 25% and the remaining four at a loss of 25%. If he made a total profit of Rs. 2000, then his purchase price of a bicycle, in Rupees, was
  • (1) 6000
  • (2) 8000
  • (3) 4000
  • (4) 2000
Show solution
(3) 4000. Net = 6(0.25c) − 4(0.25c) = 0.5c = 2000 ⇒ c = 4000.
EasyCAT 2020 · TITAE3
A person spent Rs. 50000 to purchase a desktop computer and a laptop computer. He sold the desktop at 20% profit and the laptop at 10% loss. If overall he made a 2% profit, then the purchase price, in rupees, of the desktop is
Show solution
20000. 0.2d − 0.1(50000 − d) = 1000 ⇒ 0.3d = 6000 ⇒ d = 20000.
EasyCAT 2024 · Slot 3E4
Gopi marks a price on a product in order to make 20% profit. Ravi gets 10% discount on this marked price, and thus saves Rs 15. Then, the profit, in rupees, made by Gopi by selling the product to Ravi, is
  • (A) 10
  • (B) 25
  • (C) 15
  • (D) 20
Show solution
(A) 10. MP = 1.2X; 10% discount saves 0.12X = 15 ⇒ X = 125; SP = 1.08X = 135; profit = 135 − 125 = 10.
EasyCAT 2017E5
Mayank buys some candies for Rs. 15 a dozen and an equal number of different candies for Rs. 12 a dozen. He sells all for Rs. 16.50 a dozen and makes a profit of Rs. 150. How many dozens of candies did he buy altogether?
  • (1) 50
  • (2) 30
  • (3) 25
  • (4) 45
Show solution
(1) 50. Per n dozen each: cost 27n, revenue 33n, profit 6n = 150 ⇒ n = 25 ⇒ total 2n = 50.
EasyCAT 2017E6
In a market, the price of medium quality mangoes is half that of good mangoes. A shopkeeper buys 80 kg good mangoes and 40 kg medium quality mangoes from the market and then sells all these at a common price which is 10% less than the price at which he bought the good ones. His overall profit is
  • (1) 6%
  • (2) 8%
  • (3) 10%
  • (4) 12%
Show solution
(2) 8%. Good = 2u, medium = u. CP = 80·2u + 40·u = 200u. SP = 120 × 1.8u = 216u ⇒ profit = 16/200 = 8%.

Level 3 · Moderate CAT

ModerateCAT 2019M1
On selling a pen at 5% loss and a book at 15% gain, Karim gains Rs. 7. If he sells the pen at 5% gain and the book at 10% gain, he gains Rs. 13. What is the cost price of the book in Rupees?
  • (1) 95
  • (2) 85
  • (3) 80
  • (4) 100
Show solution
(3) 80. −0.05p + 0.15b = 7 and 0.05p + 0.10b = 13 ⇒ add ⇒ 0.25b = 20 ⇒ b = 80.
ModerateCAT 2019M2
A shopkeeper sells two tables, each procured at cost price p, to Amal and Asim at a profit of 20% and at a loss of 20%, respectively. Amal sells his table to Bimal at a profit of 30%, while Asim sells his table to Barun at a loss of 30%. If the amounts paid by Bimal and Barun are x and y, respectively, then (x − y)/p equals
  • (1) 1
  • (2) 1.2
  • (3) 0.50
  • (4) 0.7
Show solution
(1) 1. x = 1.2p·1.3 = 1.56p; y = 0.8p·0.7 = 0.56p; (x − y)/p = 1.
ModerateCAT 2023 · Slot 2M3
Minu purchases a pair of sunglasses at Rs. 1,000 and sells to Kanu at 20% profit. Then, Kanu sells it back to Minu at 20% loss. Finally, Minu sells the same pair of sunglasses to Tanu. If the total profit made by Minu from all her transactions is Rs. 500, then the percentage of profit made by Minu when she sold the pair of sunglasses to Tanu is
  • (1) 26%
  • (2) 31.25%
  • (3) 52%
  • (4) 35.42%
Show solution
(2) 31.25%. Minu: +200 (to Kanu), buys back at 960, sells to Tanu at S. 200 + (S − 960) = 500 ⇒ S = 1260 ⇒ profit = 300/960 = 31.25%.
ModerateCAT 2025 · Slot 1 · TITAM4
A shopkeeper offers a discount of 22% on the marked price of each chair, and gives 13 chairs to a customer for the discounted price of 12 chairs to earn a profit of 26% on the transaction. If the cost price of each chair is Rs 100, then the marked price, in rupees, of each chair is
Show solution
175. Cost of 13 = 1300. Revenue = 12 × 0.78·MP = 1.26 × 1300 = 1638 ⇒ MP = 175.
ModerateCAT 2021 · Slot 1M5
A man buys 35 kg of sugar and sets a marked price in order to make a 20% profit. He sells 5 kg at this price, and 15 kg at a 10% discount. Accidentally, 3 kg of sugar is wasted. He sells the remaining sugar by raising the marked price by p percent so as to make an overall profit of 15%. Then p is nearest to
  • (1) 31
  • (2) 25
  • (3) 22
  • (4) 35
Show solution
(2) 25. With CP/kg = 1: need total SP = 40.25; got 6 + 16.2 = 22.2; 12 kg at 1.2(1+p/100) = 18.05 ⇒ p ≈ 25.
ModerateCAT 2024 · Slot 2 · TITAM6
Bina incurs 19% loss when she sells a product at Rs. 4860 to Shyam, who in turn sells this product to Hari. If Bina would have sold this product to Shyam at the purchase price of Hari, she would have obtained 17% profit. Then, the profit, in rupees, made by Shyam is
Show solution
2160. Bina CP = 4860/0.81 = 6000; Hari's price = 6000×1.17 = 7020; Shyam = 7020 − 4860 = 2160.

Practice questions generated · up to 100

Original easy-hard warm-up drills (not CAT PYQs). Pick the levels, generate a set, reveal answers.

More CAT Questions, 15 actual PYQs

Straight from CAT papers 2017-2025. Full question text; every answer solved & code-verified. marks the hard ones.

ModerateCAT 20171
If a seller gives a discount of 15% on retail price, she still makes a profit of 2%. Which of the following ensures that she makes a profit of 20%?
  • (1) Give a discount of 5% on retail price.
  • (2) Give a discount of 2% on retail price.
  • (3) Increase the retail price by 2%.
  • (4) Sell at retail price.
Show solution
(4) Sell at retail price. 0.85·RP = 1.02·CP ⇒ CP = 0.8333·RP. For 20% profit, SP = 1.2·CP = 1.0·RP.
Hard CAT 20172
Suppose, C1, C2, C3, C4 and C5 are five companies. The profits made by C1, C2, and C3 are in the ratio 9 : 10 : 8 while the profits made by C2, C4, and C5 are in the ratio of 18 : 19 : 20. If C5 has made a profit of Rs. 19 crore more than C1, then the total profit (in Rs) made by all five companies is
  • (1) 438 crore
  • (2) 435 crore
  • (3) 348 crore
  • (4) 345 crore
Show solution
(1) 438 crore. Make C2 common: C1:C2:C3 = 81:90:72; C2:C4:C5 = 90:95:100. C5 − C1 = 19 units = 19 cr ⇒ 1 unit = 1 cr. Total = 81+90+72+95+100 = 438.
Mod-HardCAT 20173
If Fatima sells 60 identical toys at a 40% discount on the printed price, then she makes 20% profit. Ten of these toys are destroyed in fire. While selling the rest, how much discount should be given on the printed price so that she can make the same amount of profit?
  • (1) 30%
  • (2) 25%
  • (3) 24%
  • (4) 28%
Show solution
(4) 28%. SP = 0.6P = 1.2CP ⇒ CP = 0.5P. Profit (60) = 6P. 50 toys: 50P(1−d) − 30P = 6P ⇒ 1 − d = 0.72 ⇒ d = 28%.
Mod-HardCAT 20204
Anil buys 12 toys and labels each with the same selling price. He sells 8 toys initially at 20% discount on the labelled price. Then he sells the remaining 4 toys at an additional 25% discount on the discounted price. Thus, he gets a total of Rs. 2112, and makes a 10% profit. With no discounts, his percentage of profit would have been:
  • (1) 55
  • (2) 60
  • (3) 54
  • (4) 50
Show solution
(4) 50. 8(0.8L) + 4(0.6L) = 8.8L = 2112 ⇒ L = 240. CP = 1920. No discount: 12×240 = 2880 ⇒ 960/1920 = 50%.
Mod-HardCAT 20185
Two types of tea, A and B, are mixed and then sold at Rs. 40 per kg. The profit is 10% if A and B are mixed in the ratio 3 : 2, and 5% if this ratio is 2 : 3. The cost prices, per kg, of A and B are in the ratio
  • (1) 17 : 25
  • (2) 18 : 25
  • (3) 19 : 24
  • (4) 21 : 25
Show solution
(3) 19 : 24. 3a+2b = 5·(40/1.10) = 2000/11; 2a+3b = 5·(40/1.05) = 4000/21. Solving ⇒ a : b = 76 : 96 = 19 : 24.
Mod-HardCAT 2021 · Slot 26
Raj invested Rs. 10000 in a fund. At the end of first year, he incurred a loss but his balance was more than Rs. 5000. This balance, when invested for another year, grew and the percentage of growth in the second year was five times the percentage of loss in the first year. If the gain of Raj from the initial investment over the two year period is 35%, then the percentage of loss in the first year is
  • (1) 10
  • (2) 5
  • (3) 70
  • (4) 15
Show solution
(1) 10. (1−a)(1+5a) = 1.35 ⇒ 5a² − 4a + 0.35 = 0 ⇒ a = 0.7 or 0.1. Balance > 5000 ⇒ a < 0.5 ⇒ 10%.
Hard CAT 2021 · Slot 27
Anil, Bobby and Chintu jointly invest in a business and agree to share the overall profit in proportion to their investments. Anil's share of investment is 70%. His share of profit decreases by Rs. 420 if the overall profit goes down from 18% to 15%. Chintu's share of profit increases by Rs. 80 if the overall profit goes up from 15% to 17%. The amount, in Rs, invested by Bobby is
  • (1) 2200
  • (2) 2400
  • (3) 1800
  • (4) 2000
Show solution
(4) 2000. 0.7T(0.03) = 0.021T = 420 ⇒ T = 20000. Chintu: c·T·0.02 = 80 ⇒ c = 0.2. Bobby = 0.1 ⇒ 2000.
Hard · TITACAT 2021 · Slot 18
Amal purchases some pens at Rs. 8 each. To sell these, he hires an employee at a fixed wage. He sells 100 of these pens at Rs. 12 each. If the remaining pens are sold at Rs. 11 each, then he makes a net profit of Rs. 300, while he makes a net loss of Rs. 300 if the remaining pens are sold at Rs. 9 each. The wage of the employee, in INR, is
Show solution
1000. 2(N−100) = 600 ⇒ N = 400. 1200 + 300·11 − (8·400 + W) = 300 ⇒ W = 1000.
Hard · TITACAT 2022 · Slot 19
Amal buys 110 kg of syrup and 120 kg of juice, syrup being 20% less costly than juice, per kg. He sells 10 kg of syrup at 10% profit and 20 kg of juice at 20% profit. Mixing the remaining juice and syrup, Amal sells the mixture at Rs. 308.32 per kg and makes an overall profit of 64%. Then, Amal's cost price for the syrup, in rupees per kg, is:
Show solution
160. Total CP = 208j; SP = 1.64×208j = 341.12j. 8.8j + 24j + 200×308.32 = 341.12j ⇒ j = 200 ⇒ syrup = 0.8×200 = 160.
Hard CAT 2023 · Slot 310
A merchant purchases a cloth at a rate of Rs. 100 per metre and receives 5 cm length of cloth free for every 100 cm length of cloth purchased by him. He sells the same cloth at a rate of Rs. 110 per metre but cheats his customers by giving 95 cm length of cloth for every 100 cm length of cloth purchased by the customers. If the merchant provides a 5% discount, the resulting profit earned by him is
  • (1) 9.7%
  • (2) 15.5%
  • (3) 4.2%
  • (4) 16%
Show solution
(2) 15.5%. Cost/cm = 100/105. Revenue/cm = (110×0.95)/95 = 1.10. Profit = (1.10 ÷ (100/105) − 1) = 15.5%.
Hard CAT 2023 · Slot 111
Gita sells two objects A and B at the same price such that she makes a profit of 20% on object A and a loss of 10% on object B. If she increases the selling price such that objects A and B are still sold at an equal price and a profit of 10% is made on object B, then the profit made on object A will be nearest to
  • (1) 42%
  • (2) 49%
  • (3) 45%
  • (4) 47%
Show solution
(4) 47%. 1.2·CPa = 0.9·CPb ⇒ CPb = (4/3)CPa. New equal SP = 1.1·CPb = (44/30)CPa ⇒ profit on A = 46.67% ≈ 47%.
Hard · TITACAT 2023 · Slot 212
Jayant bought a certain number of white shirts at the rate of Rs. 1,000 per piece and a certain number of blue shirts at the rate of Rs. 1,125 per piece. For each shirt, he then set a fixed market price which was 25% higher than the average cost of all the shirts. He sold all the shirts at a discount of 10% and made a total profit of Rs. 51,000. If he bought both colours of shirts, then the maximum possible total number of shirts that he could have bought is
Show solution
407. SP = 1.125 × avg cost ⇒ profit = 0.125(1000w + 1125b) = 51000 ⇒ 8w + 9b = 3264. Max w + b ⇒ b minimum multiple of 8 = 8, w = 399 ⇒ 407.
Hard CAT 2024 · Slot 113
The selling price of a product is fixed to ensure 40% profit. If the product had cost 40% less and had been sold for 5 rupees less, then the resulting profit would have been 50%. The original selling price, in rupees, of the product is
  • (A) 15
  • (B) 14
  • (C) 10
  • (D) 20
Show solution
(B) 14. CP = X, SP = 1.4X. 1.5(0.6X) = 1.4X − 5 ⇒ 0.9X = 1.4X − 5 ⇒ 0.5X = 5 ⇒ X = 10 ⇒ SP = 14.
Hard CAT 2025 · Slot 214
An item with a cost price of Rs. 1650 is sold at a certain discount on a fixed marked price to earn a profit of 20% on the cost price. If the discount was doubled, the profit would have been Rs. 110. The rate of discount, in percentage, at which the profit percentage would be equal to the rate of discount, is nearest to
  • (A) 16
  • (B) 18
  • (C) 14
  • (D) 12
Show solution
(C) 14. SP₁ = 1980 = M(1−d); SP₂ = 1760 = M(1−2d) ⇒ Md = 220, M = 2200, d = 10%. Set profit% = discount r: 2200(1−r) − 1650 = 1650r ⇒ r ≈ 14.28 ≈ 14.
Mod-HardCAT 2025 · Slot 315
The monthly sales of a product from January to April were 120, 135, 150 and 165 units, respectively. The cost price of the product was Rs. 240 per unit, and a fixed marked price was used for the product in all the four months. Discounts of 20%, 10% and 5% were given on the marked price per unit in January, February and March, respectively, while no discounts were given in April. If the total profit from January to April was Rs. 138825, then the marked price per unit, in rupees, was
  • (A) 525
  • (B) 510
  • (C) 520
  • (D) 515
Show solution
(A) 525. Revenue = (120·0.8 + 135·0.9 + 150·0.95 + 165)·MP = 525·MP. Cost = 240·570 = 136800. 525·MP − 136800 = 138825 ⇒ MP = 525.