Commercial Mathematics - 02

Profit & Loss

Cost Price, Selling Price, Profit & Loss

The terms profit and loss are used in business transactions. A merchant buys goods at a price to sell to customers. The price at which he/she buys the goods is its cost price (C.P.). He/She sells the goods at a price to the customer, which is known as the selling price (S.P.).

The difference between the selling price and the cost price determines the profit or loss the merchant makes. If S.P. > C.P., the merchant makes a profit of (S.P. – C.P.). If S.P. < C.P., the merchant makes a loss of (C.P. – S.P.).

However, it is not enough to merely know the actual value of profit/loss – it is important to consider the size of profit/loss in proportion to the cost of the goods. For this reason, profit/loss is often determined as a percentage of the cost price.

Hence, a profit of `100 on an item with a C.P. of `1000 might appear greater in absolute terms when compared with a profit of `50 on another item worth `100, but in the former case, profit percentage is 10% ( = 100 1000 × 100 % ) , while in the latter case it is as high as 50% ( = 50 1000 × 100 % ) .

If the merchant makes a profit, the formula for calculating the profit percentage is:

profit   % = ( S.P.  −  C.P. C.P. × 100 )   %

If the merchant makes a loss, the formula for calculating the loss percentage is:

loss   % = ( C.P.  −  S.P. C.P. × 100 )   %

Of course, you can always use only Eq. , in which case if there is a negative value for the profit percentage, it is equivalent to a loss percentage.

If toys are bought at `80 each, and sold at `89 each, what is the profit percentage?

I sell 20 articles for the same money as I paid for 25. What is my profit percent on my outlay? Chakravarti, Arithmetic, p. 390 Example 182: 13)

Overheads , Discounts, Gross and Net

An overhead is the additional cost which is added to the C.P. of an item purchased by a merchant to arrive at a new C.P., which reflects the true cost incurred by him/her. These additional costs are a result of extra operations like transportation and storage of items.

A discount is the reduction in the selling price of an item which a merchant offers to a customer. It is almost always expressed as a percentage of the advertised price, which is known as the marked price (M.P.) or list price (L.P.). The amount that the customer pays to the merchant after the discount (M.P. - discount) is called the net price, which is the S.P. of the item.

So, an item which is available at a list price of `200 with a discount percentage of 10% will have a discount amount of `20 ( = 10 100   ×   200 ) and a net price, which the customer pays, of Rs180 (= 200 - 20).

Thus,

discount = M.P.  −  S.P.

discount   % = ( discount M.P. × 100 )   % = ( M.P.  −  S.P. M.P. × 100 )   %

Sometimes, some merchants offer successive discounts on the M.P. In such cases, the first discount is calculated on the M.P. and is subtracted from it. The next discount is calculated on the resulting amount from the previous step and is again subtracted from it to yield the next amount of the article. These steps are continues till all discounts are used up, and the final amount obtained is the S.P. of the article.

Gross profit is the total profit made by the merchant in a transaction, without deducting any taxes and/or expenses. After making the deductions for taxes and/or expenses from the gross profit, what remains is the net profit.

The marked price of a book is `30. It is sold at discount of 15%. Find the discount allowed on the book and its selling price? (NCERT, Mathematics Class IX, p. 63 Example 5)

A shirt was sold for `442 after allowing a discount of 15% on the marked price. Find the marked price of the shirt. (NCERT, Mathematics Class IX,, p. 64 Example 7)

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