ICSE Class 8 Maths Arithmetical Problems Chapter 04 Profit and Loss

Profit and Loss

Let us review the basics of profit and loss.

Some Definitions

1. The price at which a buyer purchases an article is called the cost price (CP) of the article for the buyer.

2. The price at which a seller sells an article is called the selling price (SP) of the article for the seller.

3. (i) If the SP of an article is more than its CP, there is a profit for the seller.

Profit = SP - CP, profit % = \(\frac{\text{profit}}{\text{CP}} \times 100\)

(ii) If the CP of an article is more than its SP, there is a loss for the seller.

Loss = CP - SP, loss % = \(\frac{\text{loss}}{\text{CP}} \times 100\)

(iii) If there is a profit of r%, SP = CP + profit = CP + r% of CP = CP + \(\frac{r}{100}\) × CP.

\(\therefore \text{SP} = \left(1 + \frac{r}{100}\right)\text{CP}\)

(iv) If there is a loss of r%, SP = CP - loss = CP - r% of CP = CP - \(\frac{r}{100}\) × CP.

\(\therefore \text{SP} = \left(1 - \frac{r}{100}\right)\text{CP}\)

4. Overhead expenses are the additional expenses borne by a buyer on things such as transportation, rent, repair, salaries, tax and commission. These additional expenses are also called overhead charges. Overhead expenses are added to the cost price to determine the final cost price.

Example - Manish buys a cooler for Rs 7000 and spends Rs 150 on its transportation.

So, his cost price = Rs 7000 + Rs 150 = Rs 7150.

Solved Examples

Example 1 - A man buys a watch for Rs 565 and sells it for Rs 678. Find his profit and profit percentage.

Solution - Profit = SP - CP = Rs 678 - Rs 565 = Rs 113.

\(\therefore \text{profit percentage} = \frac{\text{profit}}{\text{CP}} \times 100 = \frac{113}{565} \times 100 = \frac{1}{5} \times 100 = 20.\)

Example 2 - Tabu bought a pencil box for Rs 25 and sold it for Rs 21. Find her loss and loss percentage.

Solution - Loss = CP - SP = Rs 25 - Rs 21 = Rs 4.

\(\therefore \text{loss percentage} = \frac{\text{loss}}{\text{CP}} \times 100 = \frac{4}{25} \times 100 = 16.\)

Example 3 - A shopkeeper bought toffees at the rate of 6 for Rs 5 and sold them at the rate of 5 for Rs 6.

(i) What was his profit percentage?

(ii) How many toffees would he have to sell to earn a profit of Rs 55?

Solution - (i) CP of 6 toffees = Rs 5, so CP of 1 toffee = Rs \(\frac{5}{6}\).

Also, SP of 5 toffees = Rs 6, so SP of 1 toffee = Rs \(\frac{6}{5}\).

Profit on the sale of 1 toffee = Rs \(\frac{6}{5}\) - Rs \(\frac{5}{6}\) = Rs \(\frac{11}{30}\).

\(\therefore \text{profit percentage} = \frac{\text{profit}}{\text{CP}} \times 100 = \frac{\frac{11}{30}}{\frac{5}{6}} \times 100 = \frac{11}{30} \times \frac{6}{5} \times 100 = 44.\)

(ii) A profit of Rs \(\frac{11}{30}\) is earned on the sale of 1 toffee.

\(\therefore\) a profit of Re 1 is earned on the sale of \(\frac{30}{11}\) toffees.

\(\therefore\) a profit of Rs 55 will be earned on the sale of \(\frac{30}{11} \times 55\) toffees, i.e., 150 toffees.

Hence, he would have to sell 150 toffees to earn a profit of Rs 55.

Example 4 - Salma sells 18 eggs at the price for which she buys 20 eggs. Find her profit or loss percentage.

Solution - The SP of 18 eggs = the CP of 20 eggs.

\(\therefore\) the SP of 1 egg = the CP of \(\frac{20}{18}\) eggs = the CP of \(\frac{10}{9}\) eggs.

Let the CP of 1 egg = Rs x. Then, the SP of 1 egg = the CP of \(\frac{10}{9}\) eggs = Rs \(\frac{10}{9}\) x.

\(\therefore\) SP > CP, there is a profit.

Profit on the sale of 1 egg = SP - CP = Rs \(\frac{10}{9}\) x - Rs x = Rs \(\frac{1}{9}\) x.

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