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📐 Mathematics - Class 7
Lesson 18 · Profit and Loss

Profit and Loss

MathematicsSubject
14 minEstimated read
Everything is measured from the cost price

Profit and loss percentages are always taken on the COST price. That single convention decides every answer in this unit.

The three quantities

Name What it is Short form
Cost priceWhat the seller paid to get the itemCP
Selling priceWhat the buyer actually handed overSP
Profit or lossThe difference between themSP − CP

Profit percentage is profit over CP times 100. Loss percentage is loss over CP times 100.

Never divide by the selling price

Dividing by 600 gives 16.7%, which is not what anyone in business means. CP is what the seller put at risk, so it goes underneath.

Working forwards

A 20 per cent profit means selling at 120 per cent of cost, so 1.2 × 500 gives 600 in one step. For a loss, the multiplier is less than 1.

Working backwards to the cost price

At a 20% profit, SP 600 is 120% of the cost price. So 1% is 5, and CP was 500. Taking 20% off 600 gives the wrong answer.

Discount is a different thing

Discount comes off the MARKED price, not the cost price. A shop can offer a discount and still make a profit.

A profit percentage and a loss percentage do not cancel

Two shirts sold at 900 each, one at 20% profit and one at 20% loss, is not break even. The trader loses 75 rupees.

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Worked Example 1

A shopkeeper buys a bag for Rs 500 and sells it for Rs 600.

Find the profit in rupeesSP − CP = 600 − 500 = Rs 100
Divide by the cost price100 ÷ 500 × 100 = 20% profit
Why not divide by 600?Dividing by 600 measures the gain against money that includes the gain itself.
Worked Example 2

A radio marked at Rs 1500 with a 20% discount, which cost the shop Rs 1000.

Discount comes off the MARKED price20% of 1500 = 300, so SP = Rs 1200
Now compare with the COST priceProfit = 1200 − 1000 = Rs 200
Turn it into a percentage20% profit
Two different percentages, two different basesThe discount came from 1500 and the profit from 1000. Same number here, but a coincidence.
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Activity 18.1

Run a stall for a day

What you needA notebook page ruled into five columns, and a decision about what your stall sells.
MethodFor each item write CP, marked price and discount, then work out SP, profit and profit percentage.
The trap to set for yourselfInclude one item where the discount wipes out the profit. How large a discount can you afford?
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1

Cost price (CP) is what the seller paid. Selling price (SP) is what the buyer handed over.

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1Why is profit percentage always calculated on the cost price and never on the selling price?
2What is the difference between marked price and cost price, and why does it matter?
3An item sells for Rs 600 at a 20% profit. Why is the cost price not Rs 480?
4Two shirts are sold at Rs 900 each, one at 20% profit and one at 20% loss. Why is this not break even?
5How large a discount can a shop afford to offer without making a loss?

Question 1 of 10

1Profit percentage is calculated on the
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Slide 1 of 4
Unit 18 · Profit and Loss

Profit and Loss

Mathematics · Grade 7

What You Will Be Able To Do

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Work out profit or loss and turn it into a percentage correctly

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Work backwards from a selling price to find the cost price

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Handle marked price and discount without mixing them up with cost

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See why a 20% profit and a 20% loss do not cancel out

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Profit and loss percentages are always taken on the cost price, never on the selling price. That single convention decides every answer in this unit.

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Presenter notes: Open with a question that sounds simple. A shopkeeper buys a bag for 500 rupees and sells it for 600. What percentage profit is that? Take answers before commenting, and expect both 20 per cent and about 16.7 per cent. Both look like reasonable arithmetic, but only one answers the question a trader is actually asking, and the whole unit turns on knowing which.