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REET L1+L2 · Maths

Profit and Loss (Profit-Loss)

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Profit and Loss is a guaranteed, every-time topic in REET Maths — questions built by combining cost price, selling price, discount and percentage. This page has every formula, trick and worked example in one place.

  • 4 questions in REET 2024
  • Class 7-8 level
  • 9 min read
Verified 17 September 2026

How REET asks this topic

None of REET 2024's four profit-loss questions were solvable by plugging straight into a formula — they all needed you to think 'in reverse': at what price should a good sold at a loss be resold to make a profit, working out the loss percentage from the selling price, the real combined effect of two successive discounts, and adding an extra cost like repairs into the cost price. In other words, the exam goes beyond the basic CP-SP formulas and expects you to apply them to a practical situation. In every question, correctly identifying whether a given amount is the CP, the SP, the MP, or some third quantity the question actually wants is where most of the time and marks are won or lost.

Cost price, selling price, and basic definitions

Cost Price (CP) is the amount at which an article is bought. Selling Price (SP) is the amount at which it is sold.

When SP is more than CP, there's a Profit = SP − CP. When CP is more than SP, there's a Loss = CP − SP. Profit or loss is always calculated from the difference between the cost price and the selling price — never from the marked price.

All the essential profit-loss formulas

QuantityFormula
ProfitSelling Price (SP) − Cost Price (CP), when SP > CP
LossCost Price (CP) − Selling Price (SP), when CP > SP
Profit percentage(Profit ÷ CP) × 100
Loss percentage(Loss ÷ CP) × 100
SP, when profit % is knownCP × (100 + profit%) ÷ 100
SP, when loss % is knownCP × (100 − loss%) ÷ 100
CP, when SP and profit % are knownSP × 100 ÷ (100 + profit%)
CP, when SP and loss % are knownSP × 100 ÷ (100 − loss%)

Profit % and loss % are always calculated on the cost price (CP), never on the selling price.

Marked price and discount

Marked Price (MP) is the price a shopkeeper prints or tags on an item. Discount = MP − SP, and discount percentage = (Discount ÷ MP) × 100. So SP = MP × (100 − discount%) ÷ 100.

When two successive discounts are given on an item one after another, adding them up directly is wrong. For example, the combined effect of a 10% and a 20% discount is not the same as a 30% discount — it's less, because the second discount applies to the price already reduced by the first discount, not to the full marked price.

When an extra expense gets added to the cost price

Often an extra expense — repair, carriage, or packing — is incurred on an article after it's bought. In such a case, this extra expense is added to the article's original cost price to get the total (effective) cost price, and profit or loss is based on this total cost price, not on the purchase price of the article alone.

Example: if an old item is bought for ₹600 and ₹150 is spent on repairing it, the total cost price is taken as ₹750 — profit or loss is worked out on this ₹750, not on ₹600 alone. Similarly, carriage charges, packing costs and installation fees are always added into the cost price, because they are costs of making the item ready for sale.

A common trap: two items, same selling price, same % profit-loss

A classic trap question shows up in exams like REET: two items are sold at the same selling price, one at an x% profit and the other at an x% loss. In this situation, the trader never breaks even — there is always an overall loss, and that loss percentage equals (x/10)².

Example: if two items are sold for ₹990 each, one at a 10% profit and the other at a 10% loss, the total loss % = (10/10)² = 1%. This is worth remembering because students superficially assume that equal profit and loss cancel out to no loss at all, when in fact there is always a net loss.

How to teach children

Classroom activity

Set up a pretend 'market' in class and let children buy and sell items with play money, then have them write down CP and SP for every deal and work out the profit or loss themselves. In a larger group, give each child a different role (buyer/seller) and let them bargain, so the idea of a discount emerges naturally.

Teaching aids

Real shop price tags, discount advertisements/flyers, and 100-block models to show percentages visually. Shading percentages of profit/loss on a 10×10 grid on graph paper also helps.

Common misconception

Students often work out profit-loss percentage on the selling price (SP), when it should always be on the cost price (CP). Many children also confuse the marked price (MP) with the selling price (SP), and add two successive discounts directly, which is incorrect.

Assessment idea

Show a real advertisement or a bill and ask — 'what's the CP here, what's the SP, was there a profit or a loss, and by what percentage?' — this tests practical understanding. Quick oral examples with an immediate answer also test both speed and accuracy.

Memory trick / exam tip

Profit or loss percentage is always worked out on the cost price (CP), no matter how the question phrases it. While solving, assume CP = 100 and work the whole problem in ratios — this makes even answers with complicated fractions easy to find.

Questions asked in REET 2024 (with solutions)

Question 91

By selling a chair for ₹ 1,080, the shopkeeper suffers a loss of 10%. For how much should he sell this chair so that he gets 10% profit ?

  1. A₹ 1,200
  2. B₹ 1,400
  3. C₹ 1,100
  4. D₹ 1,320

Explanation

10% हानि पर विक्रय मूल्य ₹1,080 है, अतः क्रय मूल्य = 1080 × 100/90 = ₹1,200। 10% लाभ के लिए विक्रय मूल्य = 1200 × 110/100 = ₹1,320। विकल्प (A) ₹1,200 तो क्रय मूल्य है, विक्रय मूल्य नहीं।

Question 97

What is the loss percentage when a watch is bought for ₹ 1,260 and sold for ₹ 1,197 ?

  1. A4%
  2. B5%
  3. C7%
  4. D10%

Explanation

हानि = 1260 − 1197 = ₹63। हानि प्रतिशत = (63/1260) × 100 = 5%। (हानि प्रतिशत हमेशा क्रय मूल्य पर निकाला जाता है।)

Question 110

By giving 10% discount on an item there is a profit of 20%. If this discount is 20%, then what will be the profit ?

  1. A6 2/3%
  2. B3 1/2%
  3. C7 1/4%
  4. D12 1/2%

Explanation

माना क्रय मूल्य 100 है, तो 20% लाभ पर विक्रय मूल्य 120। 10% छूट पर विक्रय मूल्य = अंकित मूल्य का 90%, अतः अंकित मूल्य = 120 × 100/90 = 400/3। 20% छूट पर विक्रय मूल्य = 400/3 × 80/100 = 320/3 = 106⅔। अतः लाभ = 6⅔%।

Question 111

John buys an old fridge and after getting it repaired for Rs. 1,500 and selling it for Rs. 8,100, he gets a loss of 10%. Then for how much did he buy the fridge ?

  1. A7,500 रुपये
  2. B9,000 रुपये
  3. C10,500 रुपये
  4. D8,250 रुपये

Explanation

10% हानि पर विक्रय मूल्य = कुल क्रय मूल्य का 90%। अतः कुल लागत = 8,100 × 100/90 = 9,000 रुपये। इसमें 1,500 रुपये मरम्मत के शामिल हैं, इसलिए फ्रिज का क्रय मूल्य = 9,000 − 1,500 = 7,500 रुपये। 9,000 रुपये कुल लागत है, फ्रिज की कीमत नहीं।

Practice questions

Question 1

The cost price of an article is ₹800 and a profit of 15% is made on it. Find the selling price.

  1. A₹920
  2. B₹900
  3. C₹850
  4. D₹950

Explanation

SP = CP × (100 + profit%) ÷ 100 = 800 × 115 ÷ 100 = ₹920. This is a direct, formula-based question.

Question 2

An article is sold for ₹450 at a loss of 10%. Find its cost price.

  1. A₹550
  2. B₹500
  3. C₹480
  4. D₹495

Explanation

CP = SP × 100 ÷ (100 − loss%) = 450 × 100 ÷ 90 = ₹500. This formula is used because loss percentage is always based on CP.

Question 3

An article is sold for ₹1,350 at a loss of 10%. At what price should it be sold to gain 8%?

  1. A₹1,620
  2. B₹1,600
  3. C₹1,583
  4. D₹1,650

Explanation

First, CP = 1350 × 100 ÷ 90 = ₹1,500. Now, for an 8% profit, SP = 1500 × 108 ÷ 100 = ₹1,620.

Question 4

The marked price of an article is ₹800 and a discount of 15% is given. Find the selling price.

  1. A₹680
  2. B₹700
  3. C₹650
  4. D₹720

Explanation

SP = MP × (100 − discount%) ÷ 100 = 800 × 85 ÷ 100 = ₹680.

Question 5

A shopkeeper marks an article 25% above its cost price and allows a 10% discount. Find his profit percentage.

  1. A12.5%
  2. B15%
  3. C10%
  4. D22.5%

Explanation

Take CP = 100, so MP = 125. SP = 125 × 90 ÷ 100 = 112.5. Profit = 112.5 − 100 = 12.5, so profit% = 12.5%.

Question 6

Two successive discounts of 20% and 10% are given on the marked price of an article. Find the equivalent single discount.

  1. A30%
  2. B28%
  3. C25%
  4. D32%

Explanation

Take MP = 100. After the first discount = 80, after the second discount = 80 × 90 ÷ 100 = 72. Total discount = 100 − 72 = 28%. Simply adding the two discounts to get 30% is incorrect.

Question 7

A man buys an old bicycle for ₹600 and spends ₹150 on its repairs. If he wants to gain 12% on his total cost, at what price should he sell it?

  1. A₹840
  2. B₹828
  3. C₹852
  4. D₹800

Explanation

Total cost = 600 + 150 = ₹750. SP = 750 × 112 ÷ 100 = ₹840. Adding the repair cost into the cost price is essential here.

Question 8

A dealer bought a table and spent ₹200 on polishing it. He sold it for ₹2,760, making a 15% profit on his total investment. Find the original cost price of the table (before polishing).

  1. A₹2,200
  2. B₹2,400
  3. C₹2,000
  4. D₹2,160

Explanation

Total investment = 2760 × 100 ÷ 115 = ₹2,400. The table's original cost price = 2,400 − 200 = ₹2,200. Note that ₹2,400 is the total investment, not the price of the table alone.

Question 9

An article was bought for ₹250 and sold for ₹225. Find the loss percentage.

  1. A8%
  2. B10%
  3. C12%
  4. D15%

Explanation

Loss = 250 − 225 = ₹25. Loss% = (25 ÷ 250) × 100 = 10%.

Question 10

Which is the most suitable activity for a teacher while teaching profit and loss in Class 7?

  1. Aकेवल फॉर्मूले रटवाना
  2. Bकक्षा में नकली 'बाज़ार' खेल द्वारा वस्तुएँ खरीदने-बेचने की गतिविधि कराना
  3. Cबिना उदाहरण दिए सभी प्रश्न गृहकार्य में हल करने को कहना
  4. Dइस विषय को अगली कक्षा के लिए छोड़ देना

Explanation

A real-life-like activity (such as a pretend market game in class) lets children experience and understand CP, SP and profit-loss for themselves — far more effective than rote learning, and grounded in the principle of activity-based teaching.

Frequently asked questions

How many questions come from profit and loss in REET?+

REET 2024 had 4 questions from this maths topic. It's asked regularly every year, so keep both the straight formulas and reverse-type questions ready, since most questions need two or three steps rather than a single plug-in.

What is profit % and loss % always calculated on?+

Profit percentage and loss percentage are always calculated on the cost price (CP), never on the selling price (SP) — this is the most commonly misunderstood point, and exam options are deliberately built around this confusion.

What's the difference between marked price and selling price?+

Marked price is the price a shopkeeper prints on the item, while selling price is what the customer actually pays after the discount is subtracted. SP = MP − discount, and when no discount is given, MP and SP become equal.

Why is it wrong to simply add two successive discounts?+

Because the second discount applies to the price left over after the first discount, not to the whole marked price. So a 10% and a 20% discount together don't equal 30% — the actual effect (28%) is less, and this difference is exactly what exams test.

Read next

Percentage

Revise the basic rules of percentage before profit-loss.

Simple Interest

The next essential percentage-based topic — simple interest formulas.

REET Syllabus

See the complete REET Level 1 and Level 2 syllabus in one place.

REET 2024 Solved Papers

Read all of REET 2024's solved questions, subject by subject.

Change Log

  • 17 September 2026 — English page published — mirrors the fact-checked Hindi page, independently bilingual-accuracy checked