ICSE Class 7 Maths Chapter 10 Profit Loss Discount

Chapter 10

Profit, Loss And Discount

Profit And Loss

1. The cost price (C.P.) of an article is the price at which the article is bought.

2. The selling price (S.P.) of an article is the price at which the article is sold.

3. If selling price of an article is more than its cost price; it is sold at a profit (gain).

Profit = Selling Price - Cost Price

i.e., Profit (gain) = S.P. - C.P. and S.P. = C.P. + Gain

4. If selling price of an article is less than its cost price; it is sold at a loss.

Loss = Cost Price - Selling Price

i.e., Loss = C.P. - S.P. and S.P. = C.P. - Loss

5. Profit percent and loss percent are always calculated on cost price (C.P.) only.

i.e., (i) Profit % = \(\frac{\text{Profit}}{C.P.} \times 100\%\) and (ii) Loss % = \(\frac{\text{Loss}}{C.P.} \times 100\%\)

Example 1

(i) An article, bought for ₹ 120 is sold for ₹ 150. Find the gain or loss percent.

(ii) A bicycle, bought for ₹ 600 is sold for ₹ 550. Find gain or loss percent.

Solution

(i) Given: C.P. = ₹ 120 and S.P. = ₹ 150

Gain = ₹ 150 - ₹ 120 = ₹ 30

And, gain % = \(\frac{\text{Gain}}{C.P.} \times 100\% = \frac{30}{120} \times 100\% = 25\%\)

(ii) Given: C.P. = ₹ 600 and S.P. = ₹ 550

Loss = C.P. - S.P. = ₹ 600 - ₹ 550 = ₹ 50

And, loss percent = \(\frac{\text{Loss}}{C.P.} \times 100\% = \frac{50}{600} \times 100\% = \frac{25}{3}\% = 8\frac{1}{3}\%\)

To Find Selling Price (When C.P. And Profit% Or Loss% Are Known)

Example 2

(i) Geeta bought a watch for ₹ 450. For how much should she sell it to gain 10%?

(ii) Rahul bought an article for ₹ 800 and sold it at 25% loss. Find the selling price.

Solution

(i) Given: C.P. = ₹ 450

Gain = 10% of C.P. = \(\frac{10}{100} \times ₹ 450 = ₹ 45\)

And, Selling Price = Cost price + Gain

= ₹ 450 + ₹ 45 = ₹ 495

Alternative method (Direct method)

Gain = 10% implies S.P. = 110% of C.P.

S.P. = 110% of ₹ 450 = \(\frac{110}{100} \times ₹ 450 = ₹ 495\)

(iii) C.P. = ₹ 800 and loss = 25% of ₹ 800 = \(\frac{25}{100} \times ₹ 800 = ₹ 200\)

Selling price = Cost price - Loss = ₹ 800 - ₹ 200 = ₹ 600

Alternative method

Loss = 25% implies S.P. = 75% of C.P.

i.e., selling price = \(\frac{75}{100} \times ₹ 800 = ₹ 600\)

Remember

1. If gain = 20%, S.P. = 120% of C.P., i.e., \(S.P. = \frac{120}{100} \times C.P.\)

2. If loss = 20%, S.P. = 80% of C.P., i.e., \(S.P. = \frac{80}{100} \times C.P.\)

Note: Some times, the selling price and the cost price are given for different number of articles, then to find loss or gain percent, first of all, find the cost price and the selling price of equal number of articles.

Examples 3

A shopkeeper buys 50 pencils for ₹ 80 and sells them at 40 pencils for ₹ 90. Find his gain or loss percent.

Solution

Since, C.P. of 50 pencils = ₹ 80 hence, C.P. of 1 pencil = \(₹ \frac{80}{50} = ₹ 1.60\)

Since, S.P. of 40 pencils = ₹ 90 hence, S.P. of 1 pencil = \(₹ \frac{90}{40} = ₹ 2.25\)

Hence, gain = ₹ 2.25 - ₹ 1.60 = ₹ 0.65

And, Gain % = \(\frac{0.65}{1.60} \times 100\% = \frac{40}{5}\% = 5\frac{5}{8}\%\)

Teacher's Note

Understanding profit and loss helps shopkeepers determine fair prices for goods they sell, ensuring their businesses remain profitable while providing value to customers.

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