# Profit and Loss Formula

Profit and loss formulas are used to calculate the profit or loss that has been incurred by selling a particular product. They are mainly used in business and financial transactions to depict how much profit or loss a trader has incurred from any particular deal.

## What is the Profit and Loss Formula?

Profit and loss are the terms used to identify whether a transaction is profitable or not. Before moving on to the profit and loss formula, we need to understand the terms 'selling price' and 'cost price'. The price at which a product is purchased is called its cost price. The price at which a product is sold is called its selling price. Now, if the selling price is greater than the cost price, then the difference between them is called profit. If the selling price is less than the cost price, then the difference between them is called loss.

### Profit Loss Formula

When the selling price and cost price are known, the basic formula for calculating the profit is:

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

When the selling price and cost price are known, the basic formula for calculating the loss is:

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

## Derivation of Profit and Loss Formula

The derivation of the profit and loss formulas is simple to understand if the terms 'selling price' and 'cost price' are clear.

**Cost price:** The price at which an item is purchased.

**Selling price:** The price at which an item is sold.

Now, if the selling price of a product is more than its cost price, there is a profit earned in the transaction. In other words, if a product is sold at a higher price than the price at which it was bought, then a profit is earned. This is how the formula for profit is derived.

**Profit = Selling Price - Cost Price**

**Example:** Let us find the profit in a transaction if a product is bought at $20 and sold at $50. In this case, Cost price = $20; Selling price = $50. Profit = Selling Price - Cost Price

Profit = 50 - 20 = 30. Therefore, a profit of $30 is earned in the transaction.

Similarly, the formula for loss can be derived using the selling price and the cost price. In simple words, if a product is sold at a lesser price than the price at which it was bought, then we have a loss in the transaction. If the cost price of a product is more than its selling price, there is a loss is incurred in the transaction.

**Loss = Cost Price - Selling Price**

**Example: **Let us find the loss incurred if a product is bought at $60 and sold at $40. In this case, Cost price = $60; Selling price = $40. Loss = Cost Price - Selling Price

Loss = 60 - 40 = 20. Therefore, the loss incurred in the transaction is of $20.

## Formula for Profit and Loss Percentage

In some cases, after the profit or loss is calculated, it is converted in the form of a percentage. It is used to express the amount of profit or loss incurred in the form of a percentage. This helps in comparing two quantities. The formulas for profit and loss percentage are given below:

- Profit percentage(P%) = (Profit /Cost Price) × 100
- Loss percentage(L%) = (Loss / Cost price) × 100
- S.P. = {(100 + P%)/100} × CP(if SP > CP)
- S.P. = {(100 – L%)/100} × CP(if SP < CP)
- C.P. = {100/(100 + P%)} × SP(if SP > CP)
- C.P. = {100/(100 – L%)} × SP(if SP < CP)

## Examples Using Profit Loss Formula

**Example 1:**

A shopkeeper buys juice cans in bulk for $30 each. He sells them for $20 each. Using the profit loss formula, calculate the loss and the loss percentage.

**Solution:**

To find: Loss and Loss Percentage

Given: Selling price = $20; Cost price = $30

Using the profit and loss formulas, Loss = CP - SP

Loss = $30 - $20 = $10

Using Loss Percentage Formula, Loss% = (loss/CP) × 100

Loss Percentage = (10 /30) × 100

= 33.33%

**Answer: **Loss = $10 and loss percentage = 33.33%.

**Example 2:**

On selling a table for $987, Jane loses 6%. Using the profit loss formula, find out how much did she purchase it for?

**Solution:**

To find: Cost price of the table

Given: Loss Percentage = 6%; S.P. = $987

If the loss is 6%, it means that if the cost price is $100, the loss incurred is $6.

When C.P. is $100, S.P.= C.P. - Loss = 100 - 6 = $94

When S.P. is $94, C.P. = $100

When S.P. is $987, C.P. = 100/94 × 987 = $1050

**Answer: ** Cost price of the table = $1050

**Example 3:** If the cost of 6 pens is equal to the selling price of 4 pens, find the profit percent using the profit and loss formula.

**Solution:**

Let the CP of pens be a.

Then CP of 6 pens = 6a

CP of 4 pens = 4a

Given : SP of 4 pens = 6a

Using the profit and loss formulas,

Profit= SP- CP

profit = 6a - 4a = 2a

Profit % = (profit /CP) × 100

= (2a/4a)× 100 = 50%

**Answer: **Therefore, the profit % is 50%

## FAQs on Profit and Loss Formula

### What is Profit Loss Formula?

The formula used to calculate the profit in a transaction is, Profit = Selling price - Cost price, and the formula used to calculate loss is, Loss = Cost price - Selling price

### What are the Applications of the Profit and Loss Formula?

The profit and loss formulas are mainly used in business and financial transactions where the company needs to calculate the profit or loss that has been incurred in their business. On a smaller scale, these formulas can be used to calculate the profit or loss on any basic transaction in which products are purchased and sold. For example, if a shopkeeper buys a set of books for $400 and sells them at $500, then he can calculate his profit using the formula: Profit = Selling price - Cost Price. Substituting the values in the formula: $500 - $400 = $100. This shows that he earns a profit of $100 in the transaction.

### How to Derive the Profit and Loss Formula?

The profit and loss formulas can be easily derived if the terms 'selling price' and 'cost price' are understood. Cost price is the price at which an item is purchased and selling price is the price at which an item is sold. Now, if the selling price of a product is more than its cost price, there is a profit earned in the transaction. This derives the formula: Profit = Selling price - Cost Price. However, if the cost price of a product is more than its selling price, there is a loss is incurred in the transaction. This derives the formula: Loss = Cost Price - Selling Price.

### What is the Profit and Loss Percentage Formula?

The formula to calculate the profit percentage is: Profit % = Profit/Cost Price × 100. The formula to calculate the loss percentage is: Loss % = Loss/Cost Price × 100.

### Using the Profit and Loss Formula, Find the Profit Percent if the Cost of 6 Pens is Equal to the Selling Price of 4 Pens.

This question can be solved using the profit and loss formulas. Let us assume the CP of pens to be a. Then CP of 6 pens = 6a. CP of 4 pens = 4a. Given: SP of 4 pens = 6a

Profit= SP - CP

profit = 6a - 4a = 2a

Profit % = (profit /CP) × 100

= (2a/4a)× 100 = 50%. Therefore, the profit % is 50%

### What is the Selling Price Formula?

Selling price = Cost (CP) + desired profit margin (Profit). In the formula, the revenue is the selling price, the cost represents the cost of goods sold (the expenses you incur to produce or purchase goods to sell) and the desired profit margin is what you hope to earn.