The concept of Profit and Loss is very helpful in our real-time. In mathematics, we can estimate the growth of a business using its price, profit, and loss. Every product and everything has its cost price and selling price. Depending on these prices, we can estimate the profit gained or the loss incurred for a particular item. Mainly, in the Concept of Profit and Loss, we discuss the cost price, variable, fixed, and semi-variable cost, marked price, selling price, list price, margin, etc. Also, check out the profit and loss percentage formula for a better understanding.

Let us consider a shop owner selling a product. If the value of the selling price is more than the cost price of a commodity, then it is a profit and if the cost price is more than the selling price, it becomes a loss.

Also, Check:

- Examples on Calculating Profit or Loss
- Practice Test on Profit and Loss
- Word Problems on Profit and Loss

## Basic Concepts of Profit and Loss

- Check out the basic terms and concepts included in the Profit and Loss below.
- Profit (P): If the selling price of a product is more than its cost price, then the profit occurs for that product.
- Loss (L): If the selling price of a product is less than its cost price, then the loss occurs for that product.
- Cost Price (CP): The amount paid to purchase the product is known as Cost Price. It is denoted by CP. Also, the cost price classified into two different categories. They are

–> Fixed Cost: The fixed cost is constant and it doesn’t vary under any circumstances.

–> Variable Cost: It could change depending on the number of units. - Selling Price (SP): The amount of a product that can be sold is known as the Selling Price. It is denoted by SP. In some situations, the Selling Price is also called the sale price.
- Marked Price Formula (MP): The shopkeepers use Marked Price to offer a discount to the customers. The formula for Marked Price is

–> Discount = Marked Price – Selling Price

–> And Discount Percentage = (Discount/Marked price) x 100

### Profit and Loss Formulas

Let us discuss the Profit and Loss Formulas. The profit or gain is equal to the selling price minus the cost price. Also, the Loss is equal to the cost price minus the selling price.

- Profit or Gain = Selling price – Cost Price
- Loss = Cost Price – Selling Price

The formula for the profit and loss percentage is:

- Profit percentage = (Profit /Cost Price) x 100
- Loss percentage = (Loss / Cost price) x 100

Important Note:

(i) In case of profit, selling price > cost price and in case of loss, selling price< cost price.

(ii) profit or loss is usually calculated on the cost price.

(iii) The percentage value for profit and loss is calculated in terms of cost price.

### Profit and Loss Examples

- If a shopkeeper brings a shirt for Rs.120 and sells it for Rs.140, then he has made a profit of Rs.20/-.
- If a salesperson has bought a washing machine for Rs.5000 and he has to sell it for Rs.4500/-, then he has gone through a loss of Rs.500/-.
- Suppose, Sam brings a Chess Board for Rs. 300/- and she sells it to her friend for Rs. 400/-, then Sam has made a profit of Rs.100 with a gain percentage of 20%.

### Profit and Loss Tricks

Simple tricks of profit and loss make your learning easy. Along with profit and loss, remember these tricks and use them in your real life for better learning.

- Profit, P = SP – CP; SP>CP
- Loss, L = CP – SP; CP>SP
- SP = {(100 + P%)/100} x CP
- SP = {(100 – L%)/100} x CP
- CP = {100/(100 + P%)} x SP
- CP = {100/(100 – L%)} x SP
- P% = (P/CP) x 100
- L% = (L/CP) x 100
- Discount = MP – SP
- SP = MP -Discount
- For false weight, profit percentage will be P% = (True weight – false weight/ false weight) x 100.
- When you have two successful profits say x% and y%, then the net percentage profit equals (x + y + xy)/100
- When the profit is x% and loss is y%, then the net % profit or loss will be: (x – y – xy)/100
- If a product is sold at x% profit and then again sold at y% profit then the actual cost price of the product will be: CP = [100 x 100 x P/(100 + x)(100 + y)]. In case of loss, CP = [100 x 100 x P/(100 – x)(100 – y)]
- If P% and L% are equal then, P = L and %loss = P
^{2}/100

### Profit and Loss Problems with Solutions

**Example 1.**

Suppose a shopkeeper has bought 2 kg of apples for 200 rs. And sold it for Rs. 240 per kg. How much is the profit gained by him?

**Solution:**

Given that a shopkeeper has bought 2 kg of apples for 200 rs. And sold it for Rs. 240 per kg.

The Cost Price for apples is 200 rs.

The Selling Price for apples is 240 rs.

Then profit gained by shopkeeper is ; P = SP – CP

Substitute the Cost Price and Selling Price in the above formula.

P = SP – CP

P = 240 – 200 = Rs/- 40.

**Example 2.**

For the above example calculate the percentage of the profit gained by the shopkeeper.

**Solution:**

We know, Profit percentage = (Profit /Cost Price) x 100

Therefore, Profit percentage = (40/200) x 100 = 20%.

**Example 3.**

A man buys a cooler for Rs. 2000 and sells it at a loss of 30%. What is the selling price of the cooler?

**Solution:**

Given that a man buys a cooler for Rs. 2000 and sells it at a loss of 30%.

The Cost Price of the fan is Rs.2000

Loss percentage is 30%

As we know, Loss percentage = (Loss/Cost Price) x 100

Substitute the Loss and Cost Price in the above formula.

30 = (Loss/2000) x 100

Therefore, Loss = 600 rs.

As we know, Loss = Cost Price – Selling Price

So, Selling Price = Cost Price – Loss

Substitute the Loss and Cost Price in the above formula.

Selling Price = 2000 – 600

Selling Price = Rs.1400/-

Therefore, the selling price of the cooler is Rs.1400/-

**Example 4.**

If a pencil costs Rs.40 after a 10% discount, then what is the actual price or marked price of the pencil?

**Solution:**

Given that a pencil costs Rs.40 and a 10% discount.

To find out the marked price, substitute the given values in its formula.

MP x (100 – 10) /100 = 40

MP x (90/100) = 40

MP = (40 x 100)/90

MP = Rs. 44.44/-

Therefore, the actual price or marked price of the pencil is Rs. 44.44/-