Discount

Discounts are everywhere in your life. From shopping malls and e-commerce websites to financial transactions and tax calculations, you will need the concept of discount. Understanding the math behind discounts is important, whether you are a student or someone trying to purchase something.

1.0What is a Discount?

Discounts are a deduction from the price of a service or a commodity.  It is usually used to drive sales. For instance, if a shirt marked at INR 100 is available at a 20% discount, the buyer will pay only INR 80.

2.0Discount Formula

The basic discount formula is:

$\text{Discount}=\text{Marked Price}\times \frac{\text{Discount Rate}}{100}$

$\text{Selling Price}=\text{Marked Price}-\text{Discount}$

Where:

• Marked Price (MP): The original listed price.
• Discount Rate: Percentage reduction offered.
• Selling Price (SP): Final price after discount.

3.0Types of Discount

Discounts come in various forms, each serving different business and customer needs. Understanding the types of discounts can help you identify the best deals and make the most savings.

• Trade Discount

Offered by wholesalers to retailers, a trade discount is a reduction on the list price of products sold in bulk. It is not recorded in the books of accounts.

• Cash Discount

This is a reduction offered to encourage early payment. For instance, "2/10, net 30" means a 2% discount if the bill is paid within 10 days.

• Seasonal Discount

Seasonal discounts are offered during specific times of the year to attract customers.

• Quantity Discount

A quantity discount is given when goods are purchased in large volumes. It benefits both sellers (who reduce inventory) and buyers (who get more for less).

• Promotional Discount

Given during product launches or special events to drive demand and brand visibility.

4.0Calculating Discount Price

Now that we understand the types, let’s see how to apply the discount formula for calculating discount price. 

• Example 1: Single Discount

Question: A jacket is marked at INR 200 and is available at a 15% discount. What is the selling price?

$\text{Discount}=200\times \frac{15}{100}=30$

$\text{Selling Price}=200-30=INR170$

• Example 2: Successive Discounts

Question: A phone originally priced at INR 1000 is given a 10% discount, followed by an additional 5%. Find the final price.

$\text{First Discount}=1000\times \frac{10}{100}=INR100$

$\text{New price}=INR1000-INR100=INR900$

$\text{Second discount}=900\times \frac{5}{100}=INR45$

$\text{Final price}=INR900-INR45=INR855$

5.0Examples of Discount Problems

Let's explore some real-world examples of discount problems that are frequently asked in exams and interviews.

• Problem 1: Finding Discount Rate

Question: The marked price of a bag is INR 600, and it is sold for INR 540. What is the discount rate?

$\text{Discount}=600-540=60$

$\text{Discount Rate}=\frac{60}{600}\times 100=10\%$

• Problem 2: Marked Price from Selling Price

Question: A pair of shoes was sold for INR 720 after a 20% discount. What was the marked price?

Let the marked price be x.

We have,

$x-\left(\frac{20}{100}\times x\right)=720$

$x\left(1-\frac{20}{100}\right)=720$

$x\times 0.8=720$

$x=900$

6.0Discount vs Rebate: What’s the Difference?

Although the terms discount and rebate are often used interchangeably, there is a great difference between discount and rebate. 

A discount is a proactive price reduction, while a rebate is reactive and often requires additional steps. 

7.0Real-Life Applications of Discount

Understanding discounts is important not just for exams but also for real-world decisions.

• Shopping: Calculating the best deals during sales.
• Banking: Understanding interest and loan repayment schedules.
• Business: Offering trade or quantity discounts.
• Finance: Bond pricing and net present value involve discounts.
• Marketing: Designing promotional offers.