profit and loss

A shopkeeper buys goods either directly from the manufacturer or through a wholesaler. He pays a certain price for buying the goods. This price is called the Cost price. He then sells the goods to the customer. The price at which he sells the goods is called the Selling price.

If the selling price of the article exceeds the Cost price, i.e. Selling price  > Cost price, then there is a Profit or gain.

Profit = Selling price − Cost price

If the Selling price of an article is less than the Cost price, i.e. Selling price < Cost price, then there is a Loss.

Loss = Cost price − Selling price

Apart from the cost of goods, the shopkeeper has to bear the expenses like transportation, labor wages, storage charges, etc. These expenses are known as Overhead expenses and are included in the Cost price of an article.

Cost price = Purchase price + Overhead expenses

In business transactions, the profit and loss are usually expressed as a percent of the Cost price:

\(\textrm{Profit} \ \textrm{Percent} = \frac{\textrm{Profit}}{\textrm{Cost Price}} \times 100\) \(\textrm{Loss} \ \textrm{Percent} = \frac{\textrm{Loss}}{\textrm{Cost price}} \times 100\)

In order to attract customers and give a boost to the sale of an item or to clear the old stock, articles are sold at reduced prices. The reduction in price in such cases is called the discount. Discount is the amount deducted from the Marked price (the price printed on the price tag of an article).

After deducting the discount from the Marked price, the Sale price or Selling price is the price. 

When two or more discounts are applicable one after another to the marked price, they are known as successive discounts and they make a discount series. The first discount in the series is applied to the marked price, the second discount is applied to the resulting discounted price, and so on. 

Selling Price = Marked Price − Discount \(\textrm{Discount} \ \textrm{percent} = \frac{\textrm{Discount}}{\textrm{Marked price}} \times 100\)

• The Selling price for the one who sells the article is the Cost price for the other who purchases the article.
• Overhead expenses are always included in the cost price of an article.
• If a man sells an article at a loss of 10%, he will receive 90% of the Cost price, i.e. Selling price = 90% of the Cost price.
• If a man sells an article at a profit of 10%, he will receive 110% of the Cost price, i.e. Selling price = 110% of the Cost price.
• When the profit is m% and loss is n%, then the net % profit or loss will be (m−n−mn)/100.
• Discount is generally expressed as a percent of the Marked price. 
• x% discount on the Marked price of an article means the Selling price of an article is (100 − x)% of the Marked price.

Let us take a few examples and see the application of the above points:

Example 1: By selling an article at a profit of $60, a shopkeeper made a profit of 20%. Find (i) the cost price (ii) the selling price.

Solution: Let the cost price of the article is $100, then the selling price will be 100 + 20 = $120

If the profit is 20 then the cost price 100

therefore, if the profit is $60 then the cost price will be \({60 \times 100 \over 20} = 300\)

The selling price is 300 + 60 = $360

Example 2: David bought an old bike for $850 and spent \(1 \over 10\) of the cost price on its repairs. He sold the bike for $1050. Find his gain or loss percentage.

Solution: Repair charge = \({1\over 10} \times 850 = 85\), therefore, the total cost incurred is 850 + 85 = $935

The selling price of the bike is $1050, therefore total gain is 1050 - 935 = $115

Gain percent = \({100 \times 115 \over 935} = 12.3\)% (approx)