Profit And Loss As Percentage

The percentage is one of the methods for comparing two quantities. Daily we come across a variety of situations where we calculate or compare things in percent. Most common ones are the situations related to buying and selling of items. While the sale of a good, one can either gain a profit or bear a loss, which is generally calculated in terms of percentage.

Before we go through profit and loss percent, we need to familiarize ourselves with few terminologies, that are generally used in sales/purchasing of goods.

COST PRICE (CP): Cost price is the price at which we have purchased an item. This is abbreviated as CP.

SELLING PRICE (SP): Selling price is the price at which we sell an item; in short, it is written as SP.

During the purchase and sales of an item, depending upon the CP or SP, it can be either profit or loss for the seller.

PROFIT: When the Selling Price of an item is more than the Cost Price of the same item, then this is the condition of profit for the seller.

i.e. \(S.P. > C.P.\)

The difference in amount of the Selling Price and the Cost price is the net Profit, given as-

Net Profit = S.P. – C.P.

LOSS: When the Cost Price of an item is more than the Selling Price of the same item, then this is the condition of loss for the seller,

i..e. \(S.P. < C.P.\)

The difference between the amount of the Cost Price and the Selling Price is the new loss.

Net Loss = C.P. – S.P.

Example: Raj purchased a bike for Rs. 75000 and he sold it for Rs.55000. Is it the condition of profit or loss?

Solution: Given,

Cost price (CP) of the bike = Rs. 75000

Selling price (SP) of the bike = Rs.55000

Here, SP < CP, it is a loss.

Net Loss= CP – SP = 75000-55000= Rs. 20000

PROFIT & LOSS as PERCENTAGE-

Now we can easily conclude whether a sale was profitable or ended in a loss. Also, we know how to evaluate the profit or loss amount. Let’s learn how to express this amount in percentage.

Using above formulas we can always estimate what is the profit or loss amount. This can be converted in terms of percentage as well i.e. profit % or loss %. The formula for estimating profit % or loss % is as follow:

Profit % \(\mathbf{= \frac{S.P. – C.P.}{C.P.} \times 100 = \frac{Net \; Profit}{C.P.}}\times 100 \)

Loss % \( \mathbf{= \frac{C.P. – S.P.}{C.P.} \times 100 = \frac{Net \; Loss}{C.P.}}\times 100\)

Note- It is to be strictly noted that the Profit or Loss percentage is always calculated on the Cost Price of an item, until and unless it is mentioned to calculate the percentage on Selling Price.

Considering the above example, we can estimate Raj’s loss % using this formula.

\(\large \frac{20000}{75000} \times 100 = \frac{80}{3}\)

= \(26.667 \) %

Loss percent of Raj is 26.67 % .

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Practise This Question

A person sells 36 oranges per rupee and incurs a loss of 4%.  Find how many oranges are to be sold for a rupee to have a gain of 8%?