Introduction to Profit, Loss, and Discount

Every day, when we buy or sell things, we deal with prices and money. Sometimes, the price at which we buy something is different from the price at which we sell it. This difference can lead to either a profit (when we earn money) or a loss (when we lose money). Additionally, shops often offer discounts to attract customers by reducing the price from the original or marked price.

Understanding these concepts is very important, especially when you shop or run a business. In India, prices are usually in INR (Indian Rupees), and knowing how to calculate profit, loss, and discount helps you make smart decisions and solve many competitive exam problems quickly.

Basic Definitions and Relationships

Let's start by understanding some key terms:

• Cost Price (CP): The price at which an item is bought. For example, if you buy a pen for Rs.50, then Rs.50 is the cost price.
• Selling Price (SP): The price at which the item is sold. If you sell the pen for Rs.60, then Rs.60 is the selling price.
• Profit: When the selling price is more than the cost price, the extra money earned is called profit.
• Loss: When the selling price is less than the cost price, the amount lost is called loss.
• Marked Price (MP): The original price marked on an item before any discount is given.
• Discount: The reduction given on the marked price to encourage buying.

These terms relate to each other as follows:

• If there is a profit, then SP = CP + Profit
• If there is a loss, then SP = CP - Loss
• Discount is the difference between the marked price and the selling price: Discount = MP - SP

Profit and Loss Calculations

Now that we know the definitions, let's learn how to calculate profit and loss amounts and their percentages.

Calculating Profit:

If the selling price is more than the cost price, the profit is:

Profit = SP - CP

Calculating Loss:

If the selling price is less than the cost price, the loss is:

Loss = CP - SP

Profit Percentage: To understand how much profit you made relative to the cost price, use:

Profit % = (Profit / CP) x 100

Loss Percentage: Similarly, for loss percentage:

Loss % = (Loss / CP) x 100

Discount and Marked Price

Shops often mark a price on items called the Marked Price (MP). However, they may sell the item at a lower price by giving a discount. The discount is the amount reduced from the marked price.

Discount = Marked Price - Selling Price

The discount percentage tells us how much discount is given relative to the marked price:

Discount % = (Discount / Marked Price) x 100

graph TD    MP[Marked Price]    D[Discount]    SP[Selling Price]    MP -->|Minus Discount| SP    MP --> D    D -->|Reduces price| SP

Advanced Discount Problems

Sometimes, items have more than one discount applied one after another. These are called successive discounts. For example, a shop may offer 10% discount followed by another 5% discount.

The final price after two successive discounts \( d_1\% \) and \( d_2\% \) on the marked price is calculated as:

Net Price = Marked Price x (1 - d_1/100) x (1 - d_2/100)

There are two types of discounts to know:

• Trade Discount: Given by the seller to the buyer, usually to encourage bulk buying. It is deducted from the marked price.
• Cash Discount: Given for prompt payment, usually after the sale, and calculated on the selling price.

Understanding these helps solve complex problems involving multiple discounts.

Formula Bank

Worked Examples