Profit, Loss and Discount: Cost Price, Selling Price and Marked Price

By the end of this lesson you will be able to work out a profit or a loss and its percentage, find the selling price from the cost price and the cost price from the selling price, work with a marked price and one or more discounts, combine a markup with a discount, and handle two sales together.

Already confident? Skip to practice: Profit and Loss quiz

Before this: you should be able to find a percentage of an amount, work out a percentage increase or decrease, and find the original value after a change (if a price rises by 25% to ₹500, it was ₹400 before). If that feels shaky, read the Percentage lesson first.

The words, and two rules

• The cost price (CP) is what the seller paid for the article.
• The selling price (SP) is what the seller gets for it.
• If SP is more than CP, the difference is a profit (also called a gain). If SP is less than CP, the difference is a loss. If SP equals CP, there is no profit and no loss: the seller breaks even.
• The marked price (MP), also called the list price, is the price written on the label.
• A discount is the amount taken off the marked price. What the customer pays after the discount is the selling price.
• To mark up is to set the marked price above the cost price. "Marked 30% above cost" means the MP is 130% of the CP.

Two rules for the whole lesson:

1. Profit and loss percentages are worked out on the cost price, unless the question says otherwise.
2. A discount percentage is worked out on the marked price, unless the question says otherwise.

So "a profit of 20%" means the profit is 20% of the CP, and "a discount of 20%" means the discount is 20% of the MP. If a question says "a profit of 20% on the selling price", then the base is the SP. Always check what each percentage is a percentage of.

Worked examples

Read each example slowly. The first two show every step. In the later ones, some steps are left for you, with the answer just below.

Example 1: Profit, loss and their percentages

Question: (a) A shopkeeper buys a ceiling fan for ₹1,200 and sells it for ₹1,416. Find his profit and his profit percentage. (b) Ravi buys a second-hand bicycle for ₹2,500 and sells it a year later for ₹2,150. Find his loss and his loss percentage. (c) A stationery shop buys a box of 40 pens for ₹320 and sells the pens at ₹9 each. What is its profit percentage?

Part (a): a profit

1. SP is more than CP, so there is a profit. Profit = SP − CP = 1,416 − 1,200 = ₹216.
2. The profit percentage is on CP: profit ÷ CP × 100 = 216/1,200 × 100.
3. Simplify: divide the top and the bottom by 12 to get 18/100. So the profit percentage is 18%.

Part (b): a loss

1. SP is less than CP, so there is a loss. Loss = CP − SP = 2,500 − 2,150 = ₹350.
2. The loss percentage is on CP: 350/2,500 × 100.
3. Divide the top and the bottom by 25 to get 14/100. So the loss percentage is 14%.

Part (c): bought together, sold one by one

1. Find the cost of one pen: 320 ÷ 40 = ₹8.
2. The profit on one pen is 9 − 8 = ₹1.
3. Profit percentage = 1/8 × 100 = 12.5%.
4. Or compare totals: the 40 pens sell for 40 × 9 = ₹360. The profit is 360 − 320 = ₹40, and 40/320 × 100 = 12.5% again.

The principle: profit = SP − CP, and loss = CP − SP. The profit or loss percentage is the profit or loss ÷ CP × 100. CP goes on the bottom, not SP. When goods are bought and sold in different numbers, compare the price of one article, or compare the totals for the same number of articles.

A related kind of question: "The cost price of 11 articles equals the selling price of 10. Find the profit percentage." Take the CP of one article as ₹1. Then 10 articles cost ₹10 and sell for ₹11 (the cost of 11). The profit on those 10 is ₹1 on a cost of ₹10, which is 1/10 × 100 = 10%. The base is the cost of the 10 articles sold, not the cost of 11.

Example 2: The selling price from the cost price, and back again

Question: (a) An almirah costs a shopkeeper ₹6,500. At what price must he sell it to make a profit of 14%? (b) A mobile phone is sold for ₹9,890 at a profit of 15%. What did it cost? (c) A table fan is sold for ₹3,404 at a loss of 8%. What did it cost? At what price would the seller have made a profit of 6% instead?

Part (a): SP from CP

1. The profit is 14% of CP: 14/100 × 6,500 = ₹910.
2. SP = CP + profit = 6,500 + 910 = ₹7,410.
3. In one step: a 14% profit makes SP = 114% of CP, so SP = 6,500 × 114/100 = 6,500 × 1.14 = ₹7,410.

After a loss, subtract instead: a loss of 8% makes SP = 92% of CP, so multiply CP by 92/100.

Part (b): CP from SP, after a profit

1. Call the CP 100%. The profit is 15% of CP, so SP = 100% + 15% = 115% of CP.
2. So 115% of CP = ₹9,890.
3. 1% of CP = 9,890 ÷ 115 = ₹86.
4. CP = 86 × 100 = ₹8,600. Check: 15% of 8,600 is 1,290, and 8,600 + 1,290 = 9,890.

Do not take 15% of ₹9,890 and subtract it. That gives ₹8,406.50, which is wrong: the 15% was of the CP, not of the SP.

Part (c): CP from SP, after a loss, then a new SP

1. A loss of 8% leaves SP = 100% − 8% = 92% of CP.
2. So 92% of CP = ₹3,404, and 1% of CP = 3,404 ÷ 92 = ₹37.
3. CP = 37 × 100 = ₹3,700. Check: 8% of 3,700 is 296, and 3,700 − 296 = 3,404.
4. For a profit of 6%, SP must be 106% of CP. 1% of CP is ₹37, so SP = 37 × 106 = ₹3,922.

The principle: a profit of p% makes SP = (100 + p)% of CP, and a loss of l% makes SP = (100 − l)% of CP. Going forward, multiply CP by (100 + p)/100, or by (100 − l)/100 after a loss. Going back, divide SP by 100 + p (or by 100 − l) to get 1% of CP, then multiply by 100. To move from one profit or loss to another, find 1% of CP first, then multiply it by (100 + the new profit percentage), or by (100 − the new loss percentage). For a 6% profit in part (c), that is 37 × 106.

Two selling prices, one cost price. A shopkeeper sells a cooler at a loss of 4%. Had he sold it for ₹250 more, he would have made a profit of 6%. What did the cooler cost?

1. At a 4% loss, SP = 96% of CP. At a 6% profit, SP = 106% of CP.
2. The two selling prices differ by 106% − 96% = 10% of CP.
3. That difference is ₹250. So 10% of CP = ₹250, 1% of CP = ₹25, and CP = ₹2,500. Check: 96% of 2,500 is 2,400, 106% of 2,500 is 2,650, and they differ by ₹250.

The same idea works when the cost price changes too. A trader sells an article at a profit of 10%. Had he bought it for 20% less and sold it for ₹42 less, he would have made a profit of 30%. What did it cost?

1. Take the cost price as ₹100. Then SP = ₹110.
2. The new cost price would be 20% less, ₹80. A 30% profit on ₹80 is ₹24, so the new SP would be ₹80 + ₹24 = ₹104.
3. For every ₹100 of cost price, the two selling prices differ by 110 − 104 = ₹6. So the difference is 6% of the CP.
4. The real difference is ₹42. So 6% of CP = ₹42, 1% of CP = 42 ÷ 6 = ₹7, and CP = 7 × 100 = ₹700. Check: the SP is ₹770. The new CP would be ₹560 (20% less than ₹700), and a 30% profit on ₹560 is ₹168, so the new SP would be ₹728. ₹770 − ₹728 = ₹42.

When one article is described in two ways, write each selling price as a percentage of the same cost price. The rupee gap between the two selling prices is the gap between their percentages, taken of the CP.

Example 3: Marked price, discount and selling price

Question: (a) A pressure cooker is marked ₹1,850, and the shop gives a discount of 12%. Find the discount and the selling price. (b) A saree marked ₹3,200 is sold for ₹2,496. What percentage discount was given? (c) After a discount of 20%, a school bag sells for ₹1,560. What was its marked price?

1. (a) The discount is 12% of the MP: 12/100 × 1,850 = ₹222.
2. SP = MP − discount = 1,850 − 222 = ₹1,628. In one step: SP = 88% of MP = 1,850 × 0.88 = ₹1,628.
3. (b) Discount = MP − SP = 3,200 − 2,496 = ₹704.
4. The discount percentage is on MP: 704/3,200 × 100. 1% of 3,200 is 32, and 704 ÷ 32 = 22, so the discount is 22%.
5. (c) After a 20% discount, SP = 80% of MP. So 80% of MP = ₹1,560.
6. Your turn: find 1% of the MP, then the MP.

Check: 1% of MP = 1,560 ÷ 80 = ₹19.50, so MP = 19.50 × 100 = ₹1,950. Check: 20% of 1,950 is 390, and 1,950 − 390 = 1,560.

The principle: discount = MP − SP, and the discount percentage is the discount ÷ MP × 100. After a discount of d%, SP = MP × (100 − d)/100. To go back, MP = SP × 100 ÷ (100 − d). A discount alone tells you nothing about profit or loss; for that you also need the cost price.

Example 4: Two discounts, one after the other

Question: A shop takes 20% off the marked price of a ₹4,500 mixer-grinder. At the counter, it gives a further 15% off the reduced price. What does the customer pay? What single discount is the same as these two?

1. First discount: 20% of 4,500 is ₹900, so the price becomes 4,500 − 900 = ₹3,600.
2. The second discount is on the price just before it, ₹3,600, not on ₹4,500. 15% of 3,600 is ₹540, so the customer pays 3,600 − 540 = ₹3,060.
3. The total discount is 4,500 − 3,060 = ₹1,440.
4. Your turn: write ₹1,440 as a percentage of the marked price.

Check: 1,440/4,500 × 100 = 32%, not 20 + 15 = 35%. With multipliers: 0.8 × 0.85 = 0.68, so the customer pays 68% of the MP, which is a single discount of 32%.

The shortcut from the Percentage lesson works here. For two changes in a row of a% and b%, the overall change is a + b + (a × b)/100 per cent. Write an increase as a positive number and a decrease (such as a discount) as a negative number.

• Here a = −20 and b = −15.
• (a × b)/100 = (−20 × −15)/100 = 300/100 = +3. A minus times a minus is a plus.
• Overall = −20 + (−15) + 3 = −32. A negative answer is an overall decrease: here, a single discount of 32%.
• The order does not matter: 15% off and then 20% off also ends at ₹3,060.
• You may see this rule for two discounts written as a + b − (a × b)/100, with both discounts as positive numbers: 20 + 15 − 3 = 32. That is the same rule with the minus signs taken out, and it gives the same 32% discount.

Your turn: a shop gives two discounts of 10% each, one after the other. Is that the same as a single discount of 20%?

Check: −10 + (−10) + (−10 × −10)/100 = −20 + 1 = −19. It is a single discount of 19%, not 20%. With multipliers: 0.9 × 0.9 = 0.81.

The principle: each discount in a row is a percentage of the price just before it, so never just add the discounts. Multiply the multipliers (for 20% off and then 15% off, 0.8 × 0.85), or use a + b + (a × b)/100 with a minus sign for each discount. For three discounts, multiply three multipliers.

Example 5: A marked-up price with a discount

Question: (a) A shopkeeper buys a wall clock for ₹2,000. He marks it 30% above the cost price and then gives a discount of 10%. What is his profit percentage? (b) A trader buys a cupboard for ₹1,500. He wants to give his customers a discount of 4% and still make a profit of 12%. What price should he mark on it?

Part (a)

1. The markup is on CP: MP = 130% of 2,000 = ₹2,600.
2. The discount is on MP: 10% of 2,600 is ₹260, so SP = 2,600 − 260 = ₹2,340.
3. Profit = 2,340 − 2,000 = ₹340.
4. Your turn: write the profit as a percentage of the cost price.

Check: 340/2,000 × 100 = 17%, not 30 − 10 = 20%. The shortcut agrees: 30 + (−10) + (30 × −10)/100 = 20 − 3 = 17. With multipliers: 1.3 × 0.9 = 1.17.

Part (b)

1. A profit of 12% on CP needs SP = 112% of 1,500 = ₹1,680.
2. A discount of 4% on MP leaves SP = 96% of MP. So 96% of MP = ₹1,680.
3. Your turn: find the marked price.

Check: 1% of MP = 1,680 ÷ 96 = ₹17.50, so MP = ₹1,750. Check: 4% of 1,750 is 70, and 1,750 − 70 = 1,680, which is 12% more than 1,500.

The principle: three prices, three bases. A markup is a percentage of the CP, a discount is a percentage of the MP, and the profit is a percentage of the CP. Go forward from CP to MP to SP by multiplying, and back from SP to MP by dividing. When a question gives no rupees, take the CP as ₹100: in part (a), the MP is then ₹130, the SP is ₹117, and the profit is 17%.

Example 6: Two sales together

Question: (a) A shopkeeper sells two second-hand sewing machines for ₹4,500 each. On one he makes a profit of 25%; on the other he makes a loss of 25%. Does he gain or lose overall, and by what percentage? (b) A dealer buys two old scooters for ₹60,000 in all. He sells one at a profit of 15% and the other at a loss of 10%, and he breaks even overall. What did each scooter cost?

Part (a)

1. Each percentage is on that machine's own CP, so find the two cost prices first.
2. First machine: SP = 125% of its CP, so 1% of its CP = 4,500 ÷ 125 = ₹36, and its CP = ₹3,600.
3. Second machine: SP = 75% of its CP, so 1% of its CP = 4,500 ÷ 75 = ₹60, and its CP = ₹6,000.
4. Total CP = 3,600 + 6,000 = ₹9,600. Total SP = 4,500 + 4,500 = ₹9,000.
5. Your turn: is this a profit or a loss? Find its percentage.

Check: SP is less than CP, so it is a loss of 9,600 − 9,000 = ₹600. Loss percentage = 600/9,600 × 100 = 6.25%. The 25% profit and the 25% loss do not cancel, because the loss is 25% of a bigger cost price.

A shortcut for this case only: when two articles are sold at the same selling price, one at r% profit and the other at r% loss, the result is always an overall loss of (r × r)/100 per cent. Here (25 × 25)/100 = 6.25. If instead the two articles had the same cost price, an r% profit on one and an r% loss on the other would cancel exactly: no profit and no loss.

Part (b)

1. He breaks even, so the rupees he gains on one scooter equal the rupees he loses on the other: 15% of the first CP = 10% of the second CP.
2. The bigger percentage must go with the smaller cost, so the costs are in the ratio of the percentages turned round: 10 : 15, which is 2 : 3. Check with parts: 15% of 2 parts is 0.3 parts, and 10% of 3 parts is 0.3 parts.
3. Your turn: share ₹60,000 in the ratio 2 : 3.

Check: 2 + 3 = 5 parts = ₹60,000, so 1 part = ₹12,000. The first scooter cost 2 × 12,000 = ₹24,000, and the second cost 3 × 12,000 = ₹36,000. Check: 15% of 24,000 = 3,600 gained, and 10% of 36,000 = 3,600 lost.

The principle: each profit or loss percentage is a percentage of its own article's cost price. So percentages on different articles cannot simply be added, and a profit and a loss of the same percentage (such as 25% and 25%) cancel only when the cost prices are equal. Turn every percentage into rupees, add the rupees, and only then find a percentage of the total cost price.

Revision: the formulas in one place

In this table p, l and d are percentages written as plain numbers: for a 12% profit, p = 12.

Revision: multipliers worth knowing

To work backwards, divide by the same number, or multiply by the fraction turned upside down. After a profit of 12.5%, SP = 9/8 of CP, so CP = SP × 8/9.

Common mistakes

• Taking the profit percentage on SP. The fan in Example 1 made ₹216 on a CP of ₹1,200, which is 216 ÷ 1,200 × 100 = 18%. Dividing by the SP instead, 216 ÷ 1,416 × 100, gives about 15.25%. That is wrong unless the question asks for the profit on the SP.
• Taking a discount on CP. A discount is a percentage of the MP. The 10% off the wall clock in Example 5 is 10% of ₹2,600 (the MP), which is ₹260, not 10% of ₹2,000 (the CP).
• Adding discounts in a row. 20% off and then 15% off is a single discount of 32%, not 35%.
• Subtracting from SP when working backwards. A phone sold for ₹9,890 at a profit of 15% cost 9,890 × 100 ÷ 115 = ₹8,600, not ₹9,890 minus 15% of ₹9,890 (that gives ₹8,406.50).
• Subtracting the discount from the markup. A 30% markup and a 10% discount give a profit of 17%, not 20%.
• Thinking an equal profit and loss cancel. At the same SP, a 25% profit on one article and a 25% loss on another give an overall loss (6.25% in Example 6). They cancel only when the two articles have the same CP.

Next

Simple and compound interest are built on percentages too. For quick revision of this topic, keep the Profit and loss formula cheat sheet handy; it also covers kinds of question this lesson does not, such as a shopkeeper who uses false weights. When you are ready for interest, try the Simple and Compound Interest quiz.

Ready to test this lesson? Take the Profit and Loss quiz

How this was made: Drafted with AI assistance; every formula and worked figure recomputed independently; spot-checked by the editor on 23 October 2026.