Discount can be explained as a difference of the gross payment made for an article or asset and the specified list price or face value of the article or just the face value of that article / asset.
The discount amount depends upon several parameters like the time of year. For example, the amount can depend on whether it is festival time, can be regional specific, can depend upon the target population and the competition.

For instance, a particular daily use goods production company may provide a discount to clear their stock, or a general store might provide a discount closest to the expiration date of what they are stocking or even to compete with the neighbourhood corner shop.

## What is Discount?

A Discount is defined as a percent or amount of decrease in the price of an item. Discount amount = Original price – Sale priceAn asset can be anything ranging from bonds to goods which have an economic value.
The face value of an article can be defined as the stated or the nominal value of security. It can also be considered as a value on which the bank determines the interest payments. When we acquire discounts from anyone, then this information is recorded on a separate discount and credited by the seller.

### Types of Discounts:

There are three types of discounts. They are:
• Sales discounts
• Early payment discounts
• Company-wide discounts.
Sales discounts are entered on an invoice, whereas, the early payment discounts are recorded for customers who make sure to pay within a stipulated time period, company-wide discounts cover the clearance sales on excess inventory.

## What is Discount Rate?

The discount rate also called as the interest rate is used in shopping centers, clothing stores, departmental stores etc. Given below is the formula used to find the discount rate.Discount Rate = $\frac{Discount}{Original Price}$ $\times$ 100%

### Examples on Discount Rate

Given below are some examples on discount rate.

Example 1:

Calculate the discount rate of an item whose original price is 50 dollars and the discount amount is 10 dollars?

Solution:

Original price = 50 dollars and discount amount = 10 dollars
Discount Rate = $\frac{Discount}{Original Price}$ $\times$ 100%
= $\frac{10}{50}$ $\times$ 100%
= 20%

Example 2:

Calculate the discount rate of an article whose original price is 34 dollars and the discount amount is 6 dollars?

Solution:

Original price = 34 dollars and discount amount = 6 dollars
Discount Rate = $\frac{Discount}{Original Price}$ $\times$ 100%
= $\frac{6}{34}$ $\times$ 100%
= 17.647%

## Word Problems on Discount

Given below are some word problems on discount.

Example 1:

A jeans costing 56 dollars is being sold for 48 dollars. Find the discount in dollars?

Solution:

Given original price of the jeans = 56 dollars and the selling price of the jeans = 48 dollars
Discount price = original price – sale price
= 56 - 48
= 8 dollars

Example 2:

Calculate the selling price of an article whose original price is 48 dollars and the discount amount is 7 dollars?

Solution:

Given the original price of the article = 48 dollars and the discount amount = 7 dollars
Discount amount = original price – sale price
Sale price = original price - discount amount
= 48 - 7
= 41 dollars

Example 3:

Calculate the selling price of an article that has a market price of 80 dollars and a discount rate of 12 %

Solution:

Given the market price (or) the original price = 80 dollars and discount rate = 12%
Discount amount = 12% of original price = $\frac{12}{100}$ × 80 = 9.6 dollars
Sale price = original price - discount amount
= 80 - 9.6
= 70.4 dollars.

Example 4:

A t-shirt costs 40 dollars and is being sold for 32 dollars. Find the discount in dollars and also the percentage of the original price?

Solution:

Given the original price of the t-shirt = 40 dollars and selling price of the t-shirt = 32 dollars
Discount = original price – sale price
= 40 – 32
= 8 dollars
Now, expressing the discount as a percentage of the original price
Discount % = $\frac{Discount\ dollars}{Original\ price}$ $\times$ 100%
Discount % = $\frac{8}{40}$ $\times$ 100% = 20%

Example 5:

The original price of a shirt is 18 dollars. The shirt is on sale for a 20% discount. What is the sale price of the shirt?

Solution:

Discount = 20% of 18 dollars
= 0.20 $\times$ (18)
= 3.60
Sale price = original price - discount Use formula to find sale price.
= 18 - 3.60
= 14.40
The sale price of the shirt is 14.40 dollars

Example 6:

The regular cost of a movie ticket is 20 dollars. On Mondays they declare a 10% discount. Calculate the discount amount and the price of the ticket on Mondays?

Solution:

Given the original price of the movie ticket = 20 dollars
The discount given on Mondays = 10% of original price
= $\frac{10}{100}$ $\times$ 20
= 0.1 $\times$ 20
= 2 dollars
So, the sale price of the movie ticket on Monday = original price of the ticket – discount given on Monday
= 20 – 2
= 18 dollars
On Monday, the price of the movie ticket = 18 dollars

Example 7:

A book store has cut down all books by 30%. If a buyer who bought a book from this shop gave 25 dollars. Calculate the original cost of this book and also find the discount price?

Solution:

Showing each of these individual quantities as percentages of the original price
Original price = Sale price + Discount
(100% of the original price) = (x% of original price) + (30% of original price)
The given discount on every book = 30%
The sale price of the buyers book = 25 dollars
So, the sale price = (100 – 30 = 70)% of the original price
Sale price = $\frac{70}{100}$ $\times$ (original price)

Original price = $\frac{100}{70}$ $\times$ (sale price)

= $\frac{100}{70}$ $\times$ (25)

= 35.714 dollars
Discount price of the book = Original price - Sale price
= 35.714 – 25
= 10.714 dollars

Example 8:

After 40% discount, the sale price of a television is 15700 dollars. Calculate the original price?

Solution:

Showing each of these individual quantities as percentages of the original price
Original price = Sale price + Discount
(100% of the original price) = (x% of original price) + (40% of original price)
Given discount on television = 40%
Sale price of television = 15700 dollars
So, the sale price = (100 – 40 = 60)% of the original price
Sale price = $\frac{60}{100}$ $\times$ (original price)

Original price = $\frac{100}{60}$ $\times$ (sale price)

= $\frac{100}{70}$ $\times$ (15700)

= 22428.571 dollars
The original price of the television = 22428.571 dollars

## Discount Practice Problems

Given below are some practice problems on discount.

Practice Problem 1: A pen costs 18 dollars and is being sold for 12 dollars. Find the discount in dollars?

Practice Problem 2: A shirt costs 50 dollars and is being sold for 28 dollars. Find the discount in dollars and also the percentage of the original price?

Practice Problem 3: After 30% discount, the sale price of a refrigerator is 14500 dollars. Calculate the original price?

Practice Problem 4: The original price of an article is 25 dollars. If it is on sale for a 30% discount. Calculate the sale price of the article?