Profit and Loss is the chapter the Punjab Police SI paper likes most for its “shop” questions: 42 of them since 2016. Almost every one is built from three prices — what the shopkeeper paid (cost price), what the sticker says (marked price) and what you actually hand over (selling price). The single idea that unlocks the chapter is this: a mark-up is always calculated on the cost price, and a discount is always calculated on the marked price. Get those two bases right and nothing else in this chapter is hard. You will learn (1) the four equations, (2) the trick of assuming CP = 100, (3) successive discounts and the “buy 2 get 1” schemes, and (4) the handful of unusual shapes the SI reuses.
The three prices
Get these in order and the chapter opens up.
If a man gains ₹15 by selling for ₹100, his cost was ₹85 — so the gain is 15/85, 17.65%, not 15%. If he loses ₹10 selling at ₹100, his cost was ₹110 and the loss is 10/110 = 9.09%. The SI has asked both of those, in the same year.
Whenever the question gives only percentages and asks for a percentage, set the cost price to 100 and walk through the story. Mark up 40% → 140. Discount 15% → 140 × 0.85 = 119. You sold at 119 against a cost of 100, so the profit is 19%. No algebra, no variables.
- A 20% mark-up and a 20% discount is not break-even. It is a 4% loss, every time.
- Transport, repair and labour are part of the cost price. ₹45,000 + ₹500 = ₹45,500.
- “Gain of x% on his outlay” means on the cost price, not on the selling price.
Ravi bought a TV set for ₹45,000 and spent ₹500 on its transportation. He sold it for ₹50,500. Find his profit percentage. (SI 29 Jun 2023)
Show answer
The cost price includes the transport: 45,000 + 500 = ₹45,500. Profit = 50,500 − 45,500 = ₹5,000. Profit % = 5000/45500 × 100 = 10.99%.
The profit earned by Kapil on selling an article for ₹1,450 is the same as the loss incurred by selling the article for ₹1,280. What is the cost price of the article? (SI 20 Jun 2023)
Show answer
“Profit at ₹1,450 equals the loss at ₹1,280” means the cost price sits exactly halfway between them: CP = (1450 + 1280)/2 = ₹1,365. Whenever a question gives you two selling prices with equal profit and loss, average them.
Marked price and discount: 20 questions
Half the chapter.
A discount is a percentage off the marked price. That is the only thing to remember. If the discount is d%, the customer pays (100 − d)% of the marked price, so SP = MP × (100 − d)/100 and, read backwards, MP = SP × 100/(100 − d). Eight of the SI's twenty discount questions are nothing but that second line.
The cost price of a juicer is ₹595. A shopkeeper allows a discount of 15% and gets a profit of 10%. Find the marked price of the juicer. (SI 2 Jul 2023)
Show answer
CP = 595 and he gains 10%, so SP = 595 × 1.10 = ₹654.50. That SP is the marked price less a 15% discount: 654.50 = MP × 0.85, so MP = ₹770. Two steps: cost → selling price, then selling price → marked price.
By what percentage above the cost price should a shopkeeper mark his goods so that even after allowing a discount of 15% on the marked price he still makes a profit of 30%? (SI 20 Jun 2023)
Show answer
Let CP = 100 and the required mark-up be m. After a 15% discount the seller wants a 30% profit, so (100 + m) × 0.85 = 130 ⇒ 100 + m = 152.94 ⇒ m = 52.9%. The general rule: required mark-up = (profit wanted) scaled up by 100/(100 − discount).
Discounts of a% and b% together are equivalent to a single discount of a + b − ab/100. For 10% and 20%: 10 + 20 − 2 = 28%, not 30%. The same formula with a plus sign (a + b + ab/100) handles two successive increases — which is exactly how mark-up questions work.
A shopkeeper offers Diwali schemes as follows : a) two successive discounts of 20% and 15% b) Buy 3 Get 2 Free c) Buy 6 Get 5 Free. Find the minimum discount percentage. (SI 29 Jun 2023)
Show answer
Compare the three schemes as single discounts. (a) 20% and 15% ⇒ 20 + 15 − 3 = 32%. (b) Buy 3 get 2 free ⇒ pay for 3, take 5 ⇒ discount 2/5 = 40%. (c) Buy 6 get 5 free ⇒ pay for 6, take 11 ⇒ discount 5/11 = 45.45%. The minimum is scheme (a), 32%.
A shopkeeper marks his goods 30% above the cost price. He sold 3/5 of the goods at the marked price, and the remaining he sold at a discount of 25%. Find his gain percentage. (SI 2 Jul 2023)
Show answer
Take the cost of all the goods as 100, so MP = 130. He sells 3/5 at the marked price: 0.6 × 130 = 78. He sells 2/5 at 25% off: 0.4 × 130 × 0.75 = 39. Total received = 78 + 39 = 117 against a cost of 100, so the gain is 17%.
The shapes the SI reuses
Four patterns worth recognising on sight.
Profit % = (y − x)/x × 100. Selling 320 mangoes for the cost of 400 gives (400 − 320)/320 = 80/320 = 25% profit. The reversed version — “CP of 20 bulbs equals SP of 36 bulbs” — is a loss: (36 − 20)/36 = 44.44%. Note the base swaps: for profit divide by x, for loss divide by the larger count.
Each seller's selling price becomes the next buyer's cost price. Multiply the factors: if A gains 20% and B gains 25%, then C pays CP × 1.20 × 1.25 = CP × 1.5. With C paying ₹225, A's cost was 225/1.5 = ₹150. Never add the two percentages.
A retailer bought goods worth ₹6,000 and sold half of them at a gain of 20%. At what percentage gain must he sell the remaining goods so as to get a gain of 40% on whole? (SI 2 Jul 2023)
Show answer
Goods cost ₹6,000, and he wants ₹8,400 in all (a 40% gain). Half the goods (cost ₹3,000) sold at 20% gain bring in 3,000 × 1.20 = ₹3,600. The rest must bring 8,400 − 3,600 = ₹4,800 from a cost of ₹3,000, so the gain on them is 1,800/3,000 = 60%.
Devesh incurred a loss of 20% on selling 20 bags for ₹10,000. Now, to earn a profit of 10% on the same 20 articles, he sells them for ₹P. Find the value of P. (SI 2 Jul 2023)
Show answer
A 20% loss means he received 80% of cost: 10,000 = CP × 0.80, so CP = ₹12,500. To make a 10% profit he must sell for 12,500 × 1.10 = ₹13,750.
Also asked onceTap to open
Harsha bought a car for a certain sum and sold it at a loss of 6% on his outlay. If he had received ₹1,80,000 more, he would have gained 14% on his outlay. What did the car cost (in ₹ lakh)? (SI 18 Aug 2021)
Show answer
Let the cost be C. He sold at 0.94C. Had he got ₹1,80,000 more he would have had 1.14C. So 1.14C − 0.94C = 1,80,000 ⇒ 0.20C = 1,80,000 ⇒ C = ₹9,00,000 — the paper's answer 9 is in lakh.
A shopkeeper purchased 100 shirts at the rate of ₹20 per piece. 20 shirts were found defective. In order to make a gain of 20%, he must sell the remaining shirts at the rate of ______ per shirt. (SI 16 Oct 2022)
Show answer
100 shirts at ₹20 cost ₹2,000. A 20% gain needs ₹2,400 in all. Only 80 shirts are saleable, so each must fetch 2400/80 = ₹30.
The loss incurred on selling 18 gift articles equals to the selling price of 7 gift articles. The loss percentage is : (SI 29 Jul 2023)
Show answer
Loss on 18 = SP of 7. Let the SP of one article be s and the CP be c. 18c − 18s = 7s ⇒ 18c = 25s ⇒ s = 18c/25. Loss per article = c − 18c/25 = 7c/25, so the loss % = 7/25 = 28%.
A grocer buys 40 pens from a wholesaler at the marked price of 36 pens. If he sells these pens giving a discount of 1%, then what will be the profit percent? (SI 2 Jul 2023)
Show answer
He buys 40 pens but pays the marked price of only 36, so his cost per pen is 36/40 = 0.9 MP. He sells at a 1% discount, i.e. 0.99 MP. Profit = (0.99 − 0.9)/0.9 = 0.09/0.9 = 10%.
An article marked for ₹60,000 is available in two schemes of discount. Under scheme 1, successive discounts of 10%, 18% and 15% are offered. Under scheme 2, successive discounts of 5%, 10% and 16% are offered. Find the difference in the selling prices under the two schemes. (SI 31 Jul 2023)
Show answer
Scheme 1: 60,000 × 0.90 × 0.82 × 0.85 = ₹37,638. Scheme 2 works out to ₹43,092 by the same chain of multiplications. The difference the paper asks for is ₹5,454. Always multiply the factors, never add the discounts.
One-page revision
Read only this the night before.
| Situation | What to do |
|---|---|
| Only percentages given | Set CP = 100 and walk the story |
| Mark-up m%, discount d% | Profit % = m − d − md/100 |
| Two discounts a%, b% | Single = a + b − ab/100 |
| Buy n get k free | Discount = k/(n + k) |
| Equal profit at SP₁ and loss at SP₂ | CP = (SP₁ + SP₂)/2 |
| Sells x at the cost of y | Profit % = (y − x)/x × 100 |
| A → B → C chain | Multiply the factors, never add |
| Discount given, MP wanted | MP = SP × 100/(100 − d) |
Cost price, selling price and profit: the restTap to open
The cost price of 1 pen is ₹750 and the selling price of 1 pen is ₹600. Find the loss percentage. (SI 29 Jul 2023)
Show answer
Loss = 750 − 600 = ₹150, and loss% is always on the cost price: 150/750 × 100 = 20%.
If the selling price of an article is 4/3 times its cost price, find the profit percent. (SI 20 Jun 2023)
Show answer
SP = (4/3) CP, so the profit is CP/3 and the profit percentage is (1/3) × 100 = 33.33%. Whenever SP/CP is a fraction, subtract 1 and multiply by 100 — no numbers needed.
A man sells calculator at the rate of ₹ 560 each which includes 12 % profit. What amount of profit will he earn in 15 days if he sells 8 calculators per day ? (SI 2016)
Show answer
₹560 includes 12% profit, so the cost price is 560 ÷ 1.12 = ₹500 and the profit per calculator is ₹60. In 15 days at 8 a day he sells 120 calculators, so the profit is 120 × 60 = ₹7,200. Option A (₹8,000) comes from taking 12% of ₹560 instead of working back to the cost price.
A pen was sold for ₹78.40 at a profit of 12%. If it had been sold for ₹79.50, what would the profit or loss percentage have been? (SI 29 Jun 2023)
Show answer
Work back to the cost price first: 78.40 ÷ 1.12 = ₹70. At ₹79.50 the profit is 79.50 − 70 = ₹9.50, so the percentage is 9.50/70 × 100 = 13.57% profit. Never compare the two selling prices directly — every percentage in this chapter is on the cost price.
A shopkeeper sells a laptop and a cell phone to the same person. The cost price of the laptop is ₹35,000, while the cost price of the cell phone is ₹12,000. He makes a profit of 9% on the laptop but suffers a loss of 8% on the cell phone. What will be his overall profit/loss? (SI 14 Jul 2023)
Show answer
Take the two items separately. Profit on the laptop = 9% of 35,000 = ₹3,150. Loss on the phone = 8% of 12,000 = ₹960. Net = 3,150 − 960 = profit of ₹2,190. Never add or subtract the percentages themselves — 9% and 8% sit on different bases.
Ganesh purchased 80 kg. of Mangoes for ₹880. Due to some unavoidable reason, he had to sell the same at a loss equal to the selling price of 20 kg. At what rate he sold the mangoes? (SI 18 Aug 2021)
Show answer
Let the selling rate be ₹s per kg. The total selling price is 80s, and the loss is 880 − 80s. The question says that loss equals the selling price of 20 kg, which is 20s. So 880 − 80s = 20s, giving 100s = 880 and s = ₹8.80 per kg. Option B (₹88) is the answer with the decimal point lost — ₹88/kg would be a profit, not a loss, on a cost of ₹11/kg.
Discount and marked price: the restTap to open
If the marked price is ₹.650 and discount 10%, then the selling price is : (SI 14 Jul 2023)
Show answer
SP = MP × (1 − discount) = 650 × 0.90 = ₹585.
A clothing store has introduced a scheme of 15% discount on T-shirts. The marked price of a T-shirt is ₹2,580. What will be the selling price of this T-shirt? (SI 20 Jun 2023)
Show answer
2,580 × 0.85 = ₹2,193. A quick route: 10% is 258 and 5% is 129, so the discount is ₹387 and 2,580 − 387 = 2,193.
Rohit purchased a TV whose marked price is ₹86,700. If shopkeeper offered 23% discount on the MRP, then find the amount paid by Rohit for purchasing the TV. (SI 29 Jul 2023)
Show answer
86,700 × 0.77 = ₹66,759. Multiplying by (100 − d)% in one step is always safer than finding the discount and subtracting.
After availing of a 24% discount on the marked price of a commodity, A purchased it for ₹323/kg. What was the marked price of the commodity per kg? (SI 9 Jul 2023)
Show answer
Reverse the discount: ₹323 is 76% of the marked price, so MP = 323 ÷ 0.76 = ₹425. Dividing, not subtracting, is what undoes a percentage.
Find the rate of discount when the selling price and marked price are in the ratio 12 : 15. (SI 20 Jun 2023)
Show answer
SP : MP = 12 : 15, so SP is 12/15 = 0.8 of MP. The discount is therefore 1 − 0.8 = 20%.
The marked price of a T-shirt bought for ₹900 is fixed so that a 12% profit is obtained on it, and it is then sold at a 14% sale discount on the marked price. Find the selling price of the T-shirt. (SI 20 Jun 2023)
Show answer
The marked price is set for a 12% profit on ₹900, so MP = 900 × 1.12 = ₹1,008. Selling at a 14% discount gives 1,008 × 0.86 = ₹866.88, which is ₹866.9. Note the shop does not actually make 12% — after the discount the profit is only 866.88 − 900 = a loss of ₹33.12.
A shopkeeper sold each saree for ₹266 after allowing a 5% discount on the marked price. Had he not given the discount, he would have made a 12% profit on the cost price. What was the cost price of each saree? (SI 15 Jul 2023)
Show answer
Undo the discount: ₹266 is 95% of the marked price, so MP = 266 ÷ 0.95 = ₹280. Selling at ₹280 would have given 12% profit, so CP = 280 ÷ 1.12 = ₹250. Two reversals in a row, each a division — never a subtraction.
A refrigerator wholesaler has offered a scheme of 10% discount on its listed price. He purchased a refrigerator for ₹45,000 and still gained 15%. Find the listed price of the refrigerator. (SI 31 Jul 2023)
Show answer
He buys at ₹45,000 and gains 15%, so the selling price is 45,000 × 1.15 = ₹51,750. That selling price is 90% of the listed price, so LP = 51,750 ÷ 0.90 = ₹57,500.
The marked price of a product is ₹2,000. A salesman sells the product after giving a 10% discount and still earns a profit of 33.33%. What is the cost price of the product? (SI 29 Jun 2023)
Show answer
After a 10% discount the selling price is 2,000 × 0.90 = ₹1,800. A profit of 33.33% means SP = (4/3) CP, so CP = 1,800 × 3/4 = ₹1,350. Converting 33.33% to the fraction 1/3 turns the division into a mental step.
A shopkeeper marks his goods 25% above the C.P. and allows a discount of 40%. If he loses ₹20, find the C.P. (SI 14 Jul 2023)
Show answer
Take CP as 100. The marked price is 125, and a 40% discount gives SP = 125 × 0.60 = 75. So he loses 25 for every 100 of cost, and that loss is ₹20. Hence CP = 20 × 100/25 = ₹80. Marking up 25% and then discounting 40% is a net loss of 25%, not 15% — percentages on different bases never cancel.
The marked price of a book is ₹1,200 but the shopkeeper gets a discount of 10%. If the shopkeeper sells the book at the marked price, then the profit per cent is _____. (SI 9 Jul 2023)
Show answer
Read who gets the discount. The shopkeeper buys at 10% off, so his cost is 1,200 × 0.90 = ₹1,080. He then sells at the full ₹1,200. Profit = ₹120 on a cost of ₹1,080, which is 120/1080 × 100 = 11.11%. Option C (10.00%) is the discount rate, not the profit rate — they differ because the two percentages sit on different bases.
A trader offers the following two schemes. Which scheme(s) has/have the maximum discount percentage? 1. Two successive discounts of 10% and 20%. 2. Buy 2 get 3. (SI 29 Jun 2023)
Show answer
Compare the two as single equivalent discounts. Scheme 1: two successive discounts of 10% and 20% leave 0.90 × 0.80 = 0.72 of the price, so the discount is 28%. Scheme 2: “buy 2 get 3” means paying for 2 items and taking 3, so the customer pays 2/3 of the price — a discount of 33.33%. 33.33% beats 28%, so the answer is only 2. Successive discounts of a% and b% are never a + b; the combined figure is always smaller.
After a discount of 15% on the selling price, a seller earns a profit of 5%. By how much (in percent) should the selling price be increased in order to earn a profit of 12% after offering a discount of 12% (approximately) on the selling price? (SI 29 Jun 2023)
Show answer
Work in multiples of the cost price. In the first case a 15% discount on the selling price leaves a 5% profit: 0.85 × SP₁ = 1.05 CP, so SP₁ = (105/85) CP. In the second case 0.88 × SP₂ = 1.12 CP, so SP₂ = (112/88) CP. The required increase is SP₂/SP₁ − 1 = (112/88) ÷ (105/85) − 1 = 1.0303 − 1, which is about 3%.
Mark-up is on cost; discount is on the sticker. Two different bases — that single sentence prevents most of the wrong answers in this chapter.