Understanding Discount: The Basics

Imagine you go shopping for a new backpack that has a price tag of Rs.2,000. However, the shopkeeper tells you there's a discount offered, which means you can buy it for less than Rs.2,000. This "less price" offered by subtracting a certain amount or percentage from the original price is what we call a discount.

Before diving deeper, let's learn some basic terms you'll see often:

• List Price (or Marked Price): The original price printed on the product before any reductions. In our example, it is Rs.2,000.
• Cost Price: The price at which the shopkeeper bought the product (usually from the manufacturer or wholesaler). This helps the shopkeeper decide the selling price.
• Selling Price: The actual price at which the product is sold to you after considering any discounts.
• Discount: The reduction given on the list price, either as a fixed amount or a percentage, to attract buyers.

Discounts are given to encourage sales, clear old stock, or reward loyal customers. They help customers save money, making shopping more attractive.

Basic Discount Formula

To find out how much you save and eventually pay, we use these relationships between list price, discount, and selling price.

If the List Price is Rs.LP, and the shopkeeper offers a discount of Rs.D or discount percentage \( d\% \), your Selling Price \( SP \) is:

Since discounts are often given as percentages, you can calculate the discount amount using:

Combining both, the formula for selling price using discount percentage is:

Or mathematically,

\( SP = LP \times \left(1 - \frac{d}{100}\right) \)

Successive Discounts

Sometimes, a shop offers not just one, but multiple discounts one after another. For example, "10% off and then an additional 5% off." These are called successive discounts.

The important thing to remember: you do not simply add the discount percentages (i.e., 10% + 5% = 15%). Instead, the second discount is applied to the reduced price after the first discount.

graph TD    A[List Price = LP] --> B[Apply first discount d1%]    B --> C[Price after first discount = LP x (1 - d1/100)]    C --> D[Apply second discount d2%]    D --> E[Selling Price = LP x (1 - d1/100) x (1 - d2/100)]

The formula for selling price after successive discounts \( d_1\% \) and \( d_2\% \) is:

\( SP = LP \times \left(1 - \frac{d_1}{100}\right) \times \left(1 - \frac{d_2}{100}\right) \)

You can also find the equivalent single discount percentage \( D \% \) that gives the same final effect as successive discounts:

\( D = d_1 + d_2 - \frac{d_1 \times d_2}{100} \)

Worked Examples