ICSE Class 8 Maths Chapter 08 Profit and Loss

Chapter 8

Profit And Loss

In the previous class, you have learnt about cost price, selling price, profit, loss, profit and loss percentage, marked price, discount and discount percentage. We also solved some real life problems involving these concepts. In this chapter, we shall review and strengthen these basic ideas and solve a few tougher problems.

Profit And Loss

Cost price. The price at which an article is purchased by a dealer is called its cost price (C.P.).

Selling price. The price at which an article is sold by a dealer is called its selling price (S.P.).

Profit. If the selling price of an article is more than its cost price, then the dealer makes a profit and

profit = selling price - cost price

Loss. If the selling price of an article is less than its cost price, then the dealer suffers a loss and

loss = cost price - selling price

In solving problems on profit and loss, remember the following:

Profit = S.P. - C.P.

Loss = C.P. - S.P.

Profit percentage = \(\left(\frac{\text{profit}}{\text{cost price}} \times 100\right)\%\)

Loss percentage = \(\left(\frac{\text{loss}}{\text{cost price}} \times 100\right)\%\)

If there is a profit of p%, then

S.P. = C.P. + profit = C.P. + p% of C.P.

= C.P. + \(\frac{p}{100}\) of C.P. = \(\left(1 + \frac{p}{100}\right)\) of C.P.

Thus, S.P. = \(\left(1 + \frac{p}{100}\right)\) of C.P.

If there is a loss of l %, then

S.P. = C.P. - loss = C.P. - l % of C.P.

= C.P. - \(\frac{l}{100}\) of C.P. = \(\left(1 - \frac{l}{100}\right)\) of C.P.

Thus, S.P. = \(\left(1 - \frac{l}{100}\right)\) of C.P.

If C.P. and S.P. are given for different number of articles, first find C.P. and S.P. of equal number of articles and then calculate profit or loss percentage.

Overheads

If an article is purchased for some amount and there are some additional expenses on transportation, labour, commission etc., these are to be included in the cost price. Such expenses are called overhead expenses or overheads.

For example:

If an article is purchased for ₹570 and ₹30 are spent on its transportation, then the total cost of the article = ₹570 + ₹30 = ₹600. If the dealer sells it for ₹645, then his profit = ₹645 - ₹600 = ₹45.

Therefore Profit percentage = \(\left(\frac{45}{600} \times 100\right)\% = \frac{15}{2}\% = 7.5\%\).

Thus, overheads (if any) are always added to the original cost to get the total cost, and the profit or loss percentage is calculated on the total cost price.

Example 1

John bought a watch for ₹540 and sold it for ₹585. Find his profit and profit percentage.

Solution.

C.P. of the watch = ₹540, S.P. of the watch = ₹585

Profit = S.P. - C.P. = ₹585 - ₹540 = ₹45

Profit percentage = \(\left(\frac{\text{profit}}{\text{C.P.}} \times 100\right)\% = \left(\frac{45}{540} \times 100\right)\%\)

= \(\frac{100}{12}\% = \frac{25}{3}\% = 8\frac{1}{3}\%\).

Example 2

By selling a bike for ₹22464, Ansari incurs a loss of ₹1536. Find his loss percentage.

Solution.

S.P. of the bike = ₹22464, loss = ₹1536

Therefore C.P. of the bike = S.P. + loss = ₹22464 + ₹1536 = ₹24000

Loss percentage = \(\left(\frac{\text{loss}}{\text{C.P.}} \times 100\right)\% = \left(\frac{1536}{24000} \times 100\right)\%\)

= \(\frac{1536}{240}\% = \frac{64}{10}\% = 6.4\%\).

Example 3

Bijoy bought bananas at the rate of 5 for ₹4 and sold them at the rate of 4 for ₹5. Calculate

(i) his gain percent.

(ii) the number of bananas he should sell to earn a profit of ₹90.

Solution.

(i) C.P. of 5 bananas = ₹4

C.P. of 1 banana = ₹\(\frac{4}{5}\) = ₹0.80

S.P. of 4 bananas = ₹5

S.P. of 1 banana = ₹\(\frac{5}{4}\) = ₹1.25

Therefore Gain on the sale of one banana

= S.P. - C.P. = ₹1.25 - ₹0.80 = ₹0.45

Therefore Gain percentage = \(\left(\frac{\text{profit}}{\text{C.P.}} \times 100\right)\%\)

= \(\left(\frac{0.45}{0.80} \times 100\right)\% = \left(\frac{45}{80} \times 100\right)\%\)

= \(\frac{225}{4}\% = 56.25\%\).

(ii) Number of bananas to be sold = \(\frac{\text{total profit}}{\text{profit on one banana}}\)

= \(\frac{₹90}{₹0.45} = \frac{90}{0.45}\) = 200.

Teacher's Note

Understanding profit and loss helps students grasp everyday shopping scenarios - when a shopkeeper buys goods wholesale and sells them retail, the difference determines their earnings.

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