**Profit and Loss: Basic Concepts **

Every business, regardless of its size or nature, operates with a single goal in mind: to be profitable. To achieve this, understanding profit and loss (P&L) is crucial. In mathematical terms, P&L deals with the financial health of a business, and it can be expressed as an equation: Profit = Revenue – Expenses. Let’s break down the basic concepts of profit and loss with real-world examples to illustrate how these mathematical principles apply in business.

**Cost Price**

Cost Price (CP) is the original price at which a product or item is bought or produced. It represents the expense incurred to acquire or manufacture the product.

**Selling Price**

Selling Price (SP) is the price at which a product is sold to customers.

**Example:** If you buy a shirt for $20 (CP) and sell it for $30 (SP), the CP is $20, and the SP is $30. You make a profit of $10 ($30 – $20).

**Profit (P)**

Profit (P) is the positive financial gain that results when the selling price (SP) of a product or service more than the cost price (CP). In other words, it is the amount of money you make when you sell something for more than it cost you.

**Example:** Suppose you buy a smartphone for $500 (CP) and sell it for $600 (SP). You make a profit of $100 because the selling price is higher than the cost price.

**Loss (L)**

Loss (L) is the negative financial impact that occurs when the cost price (CP) of a product or service more than the selling price (SP). In simple terms, it means you’re selling something for less than it cost you.

**Example:** Suppose you buy a smartphone for $500 (CP) and if you sell the smartphone for $450, you incur a loss of $50 because the selling price is lower than the cost price.

**Marked Price**

The Marked Price (MP) is the original price at which a product or service is listed for sale by a seller before any discounts or negotiations. It is also commonly referred to as the list price.

The Marked Price serves as a starting point for negotiations or as a reference for discounts. In most cases, the final selling price may be lower than the Marked Price due to discounts, promotions, or negotiations between the buyer and seller.

**Example: **Let’s say a clothing store lists a winter jacket with a Marked Price (MP) of $200. This is the original price they want to sell the jacket for. However, they decide to offer a 20% discount to attract more customers. In this example, the Marked Price (MP) of the winter jacket is $200.

**Discount**

A discount is a reduction in the original price or marked price of a product or service. It is often offered by sellers or retailers as an incentive to attract customers or to promote sales. Discounts can take various forms, such as a percentage off the marked price , a fixed dollar amount off, buy-one-get-one-free offers, or other promotional deals.

**For example,** a store might offer a 20% discount on a pair of shoes, which means the customer can purchase those shoes for 20% less than the original price.

**Discount Formulas**

**Discount Amount (D) = Marked Price (MP) – Selling Price (SP)**

This formula calculates the actual discount amount in currency terms.

**Discount Percentage (Discount %) = (Discount Amount / Marked Price) x 100**

This formula calculates the discount as a percentage of the marked price.

In summary, the discount is calculated by subtracting the selling price from the marked price (D = MP – SP). The discount percentage is calculated as the discount amount divided by the marked price, multiplied by 100.

**Profit and Loss Formulas**

### Profit Formulas:

The Profit is the amount earned when the selling price (SP) of an item is greater than the cost price (CP). The formula for profit is:

Profit (P) = Selling Price (SP) – Cost Price (CP).

### Loss (L) Formulas:

Loss occurs when the selling price (SP) of an item is less than the cost price (CP). The formula for loss is:

Loss = Cost Price (CP) – Selling Price (SP)

**Profit and Loss Percentage**

### Profit Percentage Formula:

The Profit percentage is the percentage of profit earned in relation to the cost price. It is calculated using the following formula:

**For example,** if you have a profit of $50 on an item with a cost price of $200, the profit percentage would be:

So, the profit percentage is 25%.

### Loss Percentage Formula:

Loss percentage is the percentage of loss incurred in relation to the cost price. It is calculated using the following formula:

**For example,** if you have a loss of $30 on an item with a cost price of $150, the loss percentage would be:

**Profit and Loss Examples**

**Example 1: Suppose you bought a shirt for $40 and sold it for $60. Calculate the profit and profit percentage.**

**Solution**: Cost Price (CP) = $40 Selling Price (SP) = $60

Profit (P) = SP – CP P = $60 – $40 = $20

Profit Percentage = (Profit / CP) * 100 Profit Percentage = ($20 / $40) * 100 = 50%

So, the profit is $20, and the profit percentage is 50%.

**Example 2: If purchased a book for $25 but could only sell it for $20. Calculate the loss and loss percentage.**

**Solution**: Cost Price (CP) = $25 Selling Price (SP) = $20

Loss (L) = CP – SP L = $25 – $20 = $5

Loss Percentage = (Loss / CP) * 100 Loss Percentage = ($5 / $25) * 100 = 20%

So, the loss is $5, and the loss percentage is 20%.

**Example 3:Suppose You want to buy a pair of shoes with a marked price of $80, but you get a 10% discount. Calculate the discount amount and the final selling price.**

**Solution**: Marked Price (MP) = $80 Discount Percentage = 10%

Discount Amount = (Discount Percentage / 100) * MP Discount Amount = (10/100) * $80 = $8

Selling Price (SP) = MP – Discount Amount SP = $80 – $8 = $72

The discount amount is $8, and the selling price is $72.

**Example 4: If You purchased a bicycle for $150 and sold it for $180. Calculate the profit percentage or loss percentage.**

**Solution**: Cost Price (CP) = $150 Selling Price (SP) = $180

Profit (P) = SP – CP P = $180 – $150 = $30

Profit Percentage = (Profit / CP) * 100 Profit Percentage = ($30 / $150) * 100 = 20%

So, you made a profit of $30, and the profit percentage is 20%.

## FAQs

**1. What is Profit and Loss?**

Profit and loss refer to the financial outcomes of business transactions. Profit occurs when the selling price is higher than the cost price, while loss happens when the selling price is lower than the cost price.

**2. What is Cost Price (CP)?**

Cost Price (CP) is the initial cost at which a product or service is acquired or manufactured. It includes the actual cost of production, wholesale price, and additional expenses associated with obtaining the product.

**3. What is Selling Price (SP)?**

Selling Price (SP) is the amount at which a product or service is sold to customers. It is the final price that a buyer pays to purchase the item.

**4. How is Profit Calculated?**

Profit is calculated by subtracting the cost price (CP) from the selling price (SP). The formula for profit is:

Profit = SP – CP