**The concept of Profit and Loss can be explained considering the case of a shopkeeper :**

A shopkeeper purchases articles from wholesale dealers in large quantities. He purchases the articles at a lower price and sells them to the customers at a comparatively higher price.

The difference between his purchase price and the selling price is the money that he earns. Usually the selling price is more than the purchase price and the shopkeeper gains money in the transaction.

In exceptional cases the shopkeeper is forced to dispose off the articles at a lower price than the purchase price. In such cases, he loses money in the transaction. Purchase price of an article is called its **cost price**. The price at which it is sold, is called the **selling price**.

## Cost Price

The amount paid to purchase an article or the price at which an article is made is known as its **Cost Price**.

The cost price is abbreviated as **C.P**.

(Note: Generally, the overhead expenses like cartage, taxes, labour charges, etc. are included in the cost price. If overhead expenses are not included in the cost price, then Effective Cost Price = Payment made while purchasing the goods + Overhead expenses)

## Selling Price

The price at which an article is sold is known as its **Selling Price**.

The selling price is abbreviated as **S.P.**

## Profit

If the selling price (S.P.) of an article is greater than the cost price (C.P.), the difference between the selling price and cost price is called **Profit**.

Thus, if S.P. > C.P., then

Profit = S.P. – C.P.

S.P. = C.P. + Profit

C.P. = S.P. – Profit.

## Profit Percentage

The profit percent is the profit that would be obtained for a C.P. of Rs 100 i.e.,

**Profit percent** = \(\frac{Profit}{ C.P.}\) X 100

Thus, in case of Profit or Gain (i.e., if S.P. > C.P.), we have

(i) Profit = S.P. — C.P.

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

(iii) C.P. = S.P. — Profit

(iv) Profit percent = \( \frac{Profit} { C.P.} \) X 100

(v) Profit = \( \frac{ C.P. * Profit \% } { 100} \)

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

=> S.P. = C.P. + ( \(\frac{Profit \% }{ 100}\) x C.P. )

=> S.P. = \(\frac{ (100 + Profit \% ) }{ 100 }\) x C.P.

(vii) C.P. = \(\frac{ 100 * S.P.}{ (100 + Profit \% )}\)

## Loss

If the selling price (S.P.) of an article is less than the cost price (C.P.), the difference between the cost price (C.P.) and the selling price (S.P.) is called** Loss**.

Thus, if S.P. <C.P., then

=> Loss = C.P. – S.P.

=> C.P. = S.P. + Loss

=> S.P. = C.P. – Loss

## Loss Percentage

The loss percent is the loss that would be made for a C.P. of Rs 100.

That is,

** Loss percent** = \(\frac{Loss}{C.P.}\) x 100

Thus, in case of loss (i.e., when S.P. < C.P.), we have

(i) Loss = C.P. — S.P.

(ii) S.P. = C.P. –Loss

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

(iv) Loss % = \(\frac{ Loss}{ C.P.}\) X 100

(v) Loss = \(\frac{ C.P. X Loss \%}{ 100}\)

(vi) S.P. = C.P. – Loss

=> S.P. = C.P. – \(\frac{ C.P. X Loss \%}{ 100}\)

=> S.P. = (\(\frac{ 100 – Loss \%}{ 100}\)) X C.P.

(vii) C.P. = \(\frac{ 100 * S.P.}{ (100 – Loss \%)}\)

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