**Profit and Loss Formula:** In mathematics, the **profit and loss concept** is applied to check the rate of an item in the market and recognize whether the business is profitable or not. In the market, all products have a cost price or purchasing price and a selling price. You can find the obtained profit or the incurred loss in a particular commodity by knowing the cost prices and selling prices. For example, for a businessman, when the selling price is higher than the cost price of an item, then it is a profit by selling that item and when the purchase price is higher than the selling price, then it is a loss in that item. In this article, we shall discuss the basic concepts of profit and loss, the profit and loss formula, and some solved examples.

## Profit and Loss Basic Concepts

When you purchase a product in the market for a certain cost and then sell it for a different rate, you can make either a profit or a loss by doing this. It is one of the most practical concepts of mathematics. In day-to-day life, several types of transactions happen and it involves the concept of profit and loss. There are **various terms used to deal with the profit and loss concepts like the cost price of the product (C.P.), the selling price of the product (S.P.), discount on the product, marked price of the product, profit, and loss**. These terms are explained by the following points.

### Cost Price

It refers to the price **at which an item is bought in the market**. For example, if Sumit purchased a pen for Rs. 15, then here the cost price of that pen will be Rs. 15. It is **expressed as C.P.**

### Selling Price

It refers to the price **at which an item is sold in the market**. For example, if Sumit sold the pen for Rs. 20, then here the selling price of the pen will be Rs. 20. It is **expressed as S.P.**

### Profit

Within a transaction, **if the selling price of a product is more than the cost price of that particular product, then it denotes the profit**. With the help of the definition of profit, the profit earned by Sumit is Rs. 5 after selling a pen of Rs. 15 at the rate of Rs. 20. It can be solved with the help of the formula as given below.

**Profit = Selling price – Cost price**

In the above example, the Cost price of the pen was Rs. 15 and the Selling price of the pen was Rs. 20. Hence the Profit = Selling price – Cost price = 20-15 = Rs. 5.

### Loss

Within a transaction, **if the selling price of a product is lesser than the cost price of that particular product, then it denotes the loss**. For example, when a particular book is purchased for Rs. 100 and it is sold for Rs. 80, it indicates a loss of Rs. 20 in this transaction. Loss can be solved with the help of the formula given below.

**Loss = Cost price – Selling price**

In the above example, the Cost price of the book is Rs. 100 and the Selling price of the book is Rs. 80. Hence the Loss = Cost price – Selling price = 100-80 = Rs. 20.

### Marked Price

It refers to the **price fixed by the seller by putting a label on the product**. It is considered a price **at which the seller provides a discount in the market**. After applying the discount on the Marked price of the product, it is sold at a lesser price called the selling price. For example, Sanket goes to a mall for shopping where every product is given a discount offer of 50%. When the price on a stand is written as Rs.130. It implies that the Marked Price of the stand before the discount = Rs. 130.

### Discount

It refers to the **rebate or the offer provided by the shopkeepers or businessmen to attract customers to their products**. They generally provide this type of offer to customers to cope with the competition in the market and encourage the sale of products. It is **always given on the Marked price of the product**. The discount formula is mentioned below.

**Discount = Marked Price – Selling Price**

**Discount (%) = (Discount / Marked Price) × 100**

When the marked price labelled on an item is Rs. 260 and there is a 20% discount offer on it, then it implies that the customer can purchase the item at the following rate:

20% discount on marked price = (20/100) × 260

Discount offered = Rs. 52

Hence **Selling Price = Marked Price – Discount **

Selling Price = 260 − 52 = 208

## Profit and Loss Formula

If the selling price and cost price of a product is given, then the formula for finding the profit or loss is applied. The **profit formula is used when the selling price of an item is higher than the cost price of that item**. It is mentioned below.

** Profit = Selling price (S.P.) – Cost price (C.P.)**

The **loss formula is used when the cost price of an item is higher than the selling price of that item**. It is mentioned below.

** Loss = Cost price (C.P.) – Selling price (S.P.)**

In some cases or as per the need of the given questions, the calculated profit or loss is converted into a percentage. The **percentage of profit and loss tells the amount of profit earned or loss incurred in the form of a percentage**. It also assists in the comparisons of two given quantities. **The formulas for profit and loss percentages are mentioned below.**

1. Profit percentage (P%) = (Profit /Cost Price) × 100

2. Loss percentage (L%) = (Loss / Cost price) × 100

3. S.P. = {(100 + P%) / 100} × CP (if SP > CP)

4. S.P. = {(100 – L%) / 100} × CP (if SP < CP)

5. C.P. = {100 / (100 + P%)} × SP (if SP > CP)

6. C.P. = {100 / (100 – L%)} × SP (if SP < CP)

## Profit and Loss Formula Solved Examples

**Question 1: Imagine a person has purchased 2 kg of grapes for 160 rs. and sold it for rs. 90 per kg. How much is the profit obtained by that person?**

**Solution:** Given that the cost price (CP) for grapes is 160 rs. for 2 kg

The selling price (SP) for grapes is 90 rs. per kg

So the SP for 2 kg grapes = 90 x 2 = 180 rs.

Now the profit obtained by that person is P = SP – CP

Profit (P) = 180 – 160 = Rs. 20

**Question 2: Suppose a lady has bought 1 kg of bananas for 80 rs. and sold it for rs. 70 per kg. How much is the profit or loss made by that lady?**

**Solution:** Given that the cost price (CP) for bananas is 80 rs. per kg

The selling price (SP) for bananas is 70 rs. per kg

Here the SP is lesser than the CP, there is a loss incurred by that lady.

Now the loss incurred by that lady is L = CP – SP

Loss (L) = 80 – 70 = Rs. 10

**Question 3: A man buys newspapers in bulk for Rs. 12 each. He sells them for Rs. 15 each. With the help of the profit and loss formula, find the loss and the loss percentage.**

**Solution:** Given that the cost price (CP) for newspapers is 12 rs.

The selling price (SP) for newspapers is 15 rs.

Here the SP is higher than the CP, there is a profit earned by that man.

Now the profit made by that man is P = SP – CP

Profit (P) = 15 – 12 = Rs. 3

Profit percentage (P%) = (Profit / Cost Price) × 100

Profit percentage (P%) = (3 / 12) × 100 = 25 %

**Question 4: On selling a mobile phone for Rs. 15500, Sneha loses 4%. With the profit and loss formula, Calculate how much did she buy it for?**

**Solution:** Given that the selling price (SP) for a mobile phone is 15500 rs.

The loss percentage (L%) for mobile is 4%.

If the loss is 4%, it implies that in the cost price of Rs.100, the loss incurred on that item is Rs. 4.

Let us consider that C.P. is Rs. 100,

S.P.= C.P. – Loss = 100 – 4 = Rs. 96

Hence if S.P. is Rs. 96, then C.P. = Rs. 100

As per the question, S.P. is Rs. 15500, then C.P. = 100 / 96 × 15500 = Rs. 16145.8 (Approx.)

**Question 5: If the cost price of 9 pencils is equivalent to the selling price of 6 pencils, then calculate the profit per cent with the help of the profit and loss formula.**

**Solution:** Given that the Cost price (CP) of 9 pencils = Selling price (SP) of 6 pencils

Suppose the CP of pencils is x.

Then CP of 9 pencils = 9x

CP of 6 pencils = 6x

As per the question, SP of 6 pencils = 9x

With the help of the profit and loss formula,

Profit= SP- CP

Profit = 9x – 6x = 3x

Profit % = (Profit / CP) × 100

Profit % = (3x / 6x) × 100 = 50%

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