ICSE Class 8 Maths Chapter 10 Profit Loss and Discount

Chapter 10

Profit, Loss and Discount

10.1 Review

Profit

When the selling price (S.P.) of an article is more than its cost price (C.P.), the article is said to be sold at a profit (gain).

And, Profit = Selling Price - Cost Price

i.e. Profit = S.P. - C.P.

Loss

When the selling price (S.P.) of an article is less than its cost price (C.P.), the article is said to be sold at a loss.

And, Loss = Cost Price - Selling Price

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

Profit = S.P. - C.P.

(i) S.P. = C.P. + Profit

(ii) C.P. = S.P. - Profit

Loss = C.P. - S.P.

(i) S.P. = C.P. - Loss

(ii) C.P. = S.P. + Loss

Profit and Loss Percentages

Profit (gain)% = \(\frac{\text{Profit}}{\text{C.P.}} \times 100\)% and Loss % = \(\frac{\text{Loss}}{\text{C.P.}} \times 100\)%

Important Note

Profit % and loss % are always calculated on cost price.

Test Yourself

1. If C. P. = ₹ 800 and S. P. = ₹ 600

Loss = ............................. = ........... and loss % = ............................. = ..........

2. If S. P. = ₹ 600 and profit = ₹ 120

C. P. = ............................. = ........... and profit % = ............................. = ..........

3. If S. P. = ₹ 1,250 and loss = ₹ 250

C. P. = ............................. = ........... and loss % = ............................. = ..........

4. S. P. of an article is 80% of its C. P.

If C. P. = ₹ 100, S. P. = ............................. = ..........

Loss = ............................. = ........... and loss % = ............................. = ..........

5. C. P. of an article is 80% of its S. P.

If S. P. = ₹ 100, C. P. = ............................. = ..........

Profit = ............................. = ........... and profit % = ............................. = ..........

Example 1

Articles, bought at 10 for ₹ 8, are sold at 8 for ₹ 10. Find the gain percent.

Also, find the number of articles bought and sold in order to gain ₹ 144.

Solution

Whenever the cost price and the selling price are given for different number of identical articles; first of all, find the C.P. and the S.P. of equal number of articles and then calculate the profit percent or the loss percent, as the case may be.

Also, in order to have a certain gain,

the number of articles bought and sold = \(\frac{\text{Total profit}}{\text{Profit on one article}}\)

Given: C.P. of 10 articles = ₹ 8

C.P. of 1 article = \(\frac{8}{10}\) = ₹ 0.80

Also, given: S.P. of 8 articles = ₹ 10

S.P. of 1 article = \(\frac{10}{8}\) = ₹ 1.25

Profit on 1 article = S.P. - C.P. = ₹ 1.25 - ₹ 0.80 = ₹ 0.45

and, profit % = \(\frac{\text{Profit}}{\text{C.P.}} \times 100\)%

= \(\frac{₹ 0.45}{₹ 0.80} \times 100\)% = 56.25%

(Ans.)

Also, the number of articles bought and sold

= \(\frac{\text{Total profit}}{\text{Profit on one article}}\)

= \(\frac{₹ 144}{₹ 0.45}\) = 320

(Ans.)

Teacher's Note

When buying items in bulk, understanding the profit per unit helps determine how many units to sell to reach a sales target. This is commonly used by retailers planning their inventory.

10.2 Overheads

When an article is purchased at one place and is taken to some other place; an additional money for transportation, labour, packing, etc. is to be spent. This additional money spent is termed as overheads or overhead expenses.

The overheads (if any) incurred is added to the actual cost price to get the total cost price of the article and then the profit or loss is calculated on this total cost price.

Example 2

Raju goes from Agra to Delhi to buy an article, which costs ₹ 6,500 in Delhi. He sells this article in Agra for ₹ 8,000. Find his gain or loss per cent. Consider that he spends ₹ 700 on transportation, food, etc.

Solution

Given: Actual price paid for the article = ₹ 6,500

and, overhead expenses = ₹ 700

Total cost price = ₹ 6,500 + ₹ 700 = ₹ 7,200

Since, selling price = ₹ 8,000

Gain = ₹ 8,000 - ₹ 7,200

[Gain = S.P. - C.P.]

= ₹ 800

and, gain % = \(\frac{₹ 800}{₹ 7,200} \times 100\)% = \(11\frac{1}{9}\)%

(Ans.)

Teacher's Note

When starting a business, entrepreneurs must account for all expenses including transportation and labor. These overhead costs significantly affect the actual profit margin.

Example 3

A man sold his bicycle for ₹ 810; losing one-ninth of its selling price. Find:

(i) the loss

(ii) the cost price of the bicycle

(iii) the loss as percent.

Solution

(i) Since, S. P. = ₹ 810;

loss = \(\frac{1}{9} \times ₹ 810\) = ₹ 90

(Ans.)

(ii) C.P. = S.P. + loss = ₹ 810 + ₹ 90 = ₹ 900

(Ans.)

(iii) Loss % = \(\frac{\text{Loss}}{\text{C.P.}} \times 100\)%

= \(\frac{₹ 90}{₹ 900} \times 100\)% = 10%

(Ans.)

Example 4

The selling price of a table is \(\frac{27}{25}\) times its cost price. Find the loss or the profit as percent.

Solution

Let the cost price of the table = ₹ 100

Its selling price = \(\frac{27}{25} \times ₹ 100\) = ₹ 108

Profit = S.P. - C.P. = ₹ 108 - ₹ 100 = ₹ 8

Profit % = \(\frac{\text{Profit}}{\text{C.P.}} \times 100\)% = \(\frac{₹ 8}{₹ 100} \times 100\)% = 8%

(Ans.)

Algebraic Method

Let the C.P. = ₹ x

S.P. = \(\frac{27}{25}x\)

Profit = S.P. - C.P. = \(\frac{27}{25}x - ₹ x\) = \(\frac{27 - 25}{25}x\) = \(\frac{2}{25}x\)

And, profit % = \(\frac{\frac{2}{25}x}{₹ x} \times 100\)%

= \(\frac{2}{25} \times 100\)% = 8%

(Ans.)

Teacher's Note

Understanding ratios and percentages helps in comparing prices between different vendors or analyzing profit margins across different products.

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