Discounts: Definition, Types, Formulas and Solved Examples

Discounts: Discount is the difference in price between the selling price of an object and the price listed on the object (marked price). In simple words, a discount is the price offered or price reduced as compared to the original value of the object or product.

In general, shopkeepers offer discounts to customers for increasing their sales or turn their business into profit. In our real life, we can see the word “discount” in many situations like clothing shops, grocery shops, supermarkets, automobiles etc.

Definition of Discount

In simple words, a discount is the price offered or price reduced as compared to the original value of the object or product. Discount is the difference in price between the selling price of an object and the price listed on the object (marked price).

The marked price is the price of an article, which was printed on it, and it was decided by the manufacturer or the seller, without any price reduction. Selling price is the actual price, which is used to sell the article or objects. The price for which an article or object is sold after discounts in the marked price is called the selling price. Discount is always calculated only on the marked price.

In general, shop keepers offer discounts to customers for increasing their sales or turn their business into profit. Thus, a discount is one of the key concepts in business to increase sales and profit. The words “reduction” and “off” are used to describe the discount in some cases.

Formula of Discount

The discount is always calculated on marked price or listed price. Discount can be calculated by finding the difference between the selling price and the marked price of the object.
\({\rm{Discount}} = {\rm{Marked}}\,{\rm{price}}\left( {{\rm{M}}{\rm{.P}}{\rm{.}}} \right) – {\rm{Selling}}\,{\rm{price}}\left( {{\rm{S}}{\rm{.P}}{\rm{.}}} \right)\)

Selling price: Selling price is the actual price used to sell the article or objects. The price for an article or object sold after discounts in the marked price is called the selling price.

Marked price: The marked price is the price of an article, which was printed on it, and it was decided by the manufacturer or the seller, without any price reduction.

Example:
A shopkeeper sold an item after a discount of \({\rm{Rs}}{\rm{.}}\,100,\) and the price listed on the item is \({\rm{Rs}}{\rm{.}}\,120.\)
Then, the discount offered in the above situation can be calculated by finding the difference between marked price and selling price.
\({\rm{Discount}} = {\rm{M}}{\rm{.P}}. – {\rm{S}}{\rm{.P}}. = {\rm{Rs}}{\rm{.}}\,120 – {\rm{Rs}}{\rm{.}}\,100 = {\rm{Rs}}.\,20.\)

Types of Discounts

The manufactures or sellers offer discounts by selling the items. There are different types of discounts offered, which are discussed below:

Trade Discount

The distributor offers this type of discount to the retailer and not to the end customer. A distributor is one who takes vast quantities of a product. He offers these products to a retailer who runs a unit or a shop selling the product at a reduced price.

This type of discount is offered between distributors and retailers or shopkeepers. This is the first stage of discount on the marked price of an item. This type of discount helps to sell the product easily.

Quantity Discount

Quantity discounts generally happen between the retailer and the customer. Quantity discounts are offered to the customers; if a customer buys a large number of products. This type of discount is offered to the customer to attract them to buy a large quantity of products.

The retailers generally fix this type of discount. Quantity discount is the second stage of discount.

Promotional Discounts

Promotional discounts are generally offered to customers when any new product is to be promoted to increase the sales of that product. It is also offered when a stock clearance is to be done. Promotional discounts are usually promoted or advertised as offering something extra for purchasing a certain number of items.

For example, “Buy \(2\) Get \(1\)” is the most used way for a promotional discount.

Percentage Discount

The manufactures or sellers offer discounts by selling the items. Discount can be calculated by finding the difference between the selling price and the marked price of the object.

We know that a percentage discount or discount rate can always be calculated on the marked price. The formula used to calculate the discount percentage or discount rate is given below:

\({\rm{Discount}}\,{\rm{percentage}} = \frac{{{\rm{Discount}}}}{{{\rm{Marked}}\,{\rm{Price}}}} \times 100\)
\(\% \,{\rm{Discount}} = \frac{{{\rm{M}}{\rm{.P}}{\rm{.}} – {\rm{S}}{\rm{.P}}{\rm{.}}}}{{{\rm{M}}{\rm{.P}}{\rm{.}}}} \times 100\)

Therefore, percentage discount is the ratio of discount given to the product’s marked price and multiplied by \(100.\)

Example: The price marked on a book is \({\rm{Rs}}.\,10\) and the discount offered is \({\rm{Rs}}.\,2,\) then the discount percentage can be calculated as follows:
\({\rm{Discount}}\,{\rm{percentage}} = \frac{{{\rm{Rs}}.\,2}}{{{\rm{Rs}}.\,10}} \times 100 = 20\% \)

Uses of Discounts

The uses of discounts offered on the products are listed below:
1. For increasing the sales
2. To clear out the old stock present
3. To encourage distributors, sellers, etc.
4. To attract more customers etc.
Thus, the discount is offered to attract customers to increase the sales of a particular product or service. In our real life, we can see the word “discount” in many situations like clothing shops, grocery shops, supermarkets, automobiles etc.

Discount Formulas

Some of the formulas associated with discounts are listed below:

Solved Examples – Discounts

Q.1. Ramu went to the shop to buy clothes. The price tag printed on the jeans shows \({\rm{Rs}}.\,25.\) But Ramu was paid only \({\rm{Rs}}.\,20\) since there was some discount on the jeans. Find the discount percentage given.
Ans: The price printed on the jeans is \({\rm{Rs}}.\,25.\)
So, the marked price of the jeans \(\left( {{\rm{M}}{\rm{.P}}{\rm{.}}} \right){\rm{ = Rs}}.\,25.\)
But, the shopkeeper paid jeans to Ramu after some discount at the price of \({\rm{Rs}}.\,20.\)
So, the selling price of the jeans \(\left( {{\rm{S}}{\rm{.P}}{\rm{.}}} \right){\rm{ = Rs}}.\,20.\)
Thus, a discount given on the jeans is equal to the difference between the jeans’ marked price and selling price.
\({\rm{Discount}} = {\rm{M}}{\rm{.P}}{\rm{.}} – {\rm{S}}{\rm{.P}}{\rm{.}}\)
\( \Rightarrow {\rm{Discount}} = {\rm{Rs}}{\rm{.}}\,25 – {\rm{Rs}}{\rm{.}}\,20 = {\rm{Rs}}.\,5\)
Thus, discount given on the jeans is \({\rm{Rs}}.\,5\)
The discount percentage was given by the ratio of discount to the marked price, and that is multiplied by \(100.\)
\(\% \,{\rm{Discount}} = \frac{{{\rm{Discount}}}}{{{\rm{M}}{\rm{.P}}{\rm{.}}}} \times 100\)
\( \Rightarrow \,\% \,{\rm{Discount}} = \frac{{{\rm{Rs}}.\,5}}{{{\rm{Rs}}{\rm{.}}\,25}} \times 100\)
\( \Rightarrow \,\% \,{\rm{Discount}} = 5 \times 4 = 20\,\% \)
Hence, the percentage discount is given on the jeans is \(20\,\% .\)

Q.2. Preethu went to a shop to buy a television. The price marked on the television is \({\rm{Rs}}.\,25000,\) and the Preethu got a \(20\% \) discount on it. How much amount Preethu pay for the shopkeeper for television.
Ans: Given, the price marked on the television is \({\rm{Rs}}.\,25000,\)
So, \({\rm{M}}{\rm{.P}}{\rm{.}} = {\rm{Rs}}.\,25000\)
The given discount percentage on the sale of television is \(20\% .\)
We know that the discount percentage was given by the ratio of discount to the marked price multiplied by \(100.\)
\(\% \,{\rm{discount}} = \frac{{{\rm{M}}{\rm{.P}}. – {\rm{S}}{\rm{.P}}{\rm{.}}}}{{{\rm{M}}{\rm{.P}}{\rm{.}}}} \times 100\)
\( \Rightarrow 20 = \frac{{25000 – {\rm{S}}{\rm{.P}}.}}{{25000}} \times 100\)
\( \Rightarrow 20 = \frac{{25000 – {\rm{S}}{\rm{.P}}.}}{{25000}}\)
\( \Rightarrow 20 \times 250 = 25000 – {\rm{S}}{\rm{.P}}{\rm{.}}\)
\( \Rightarrow 5000 = 25000 – {\rm{S}}{\rm{.P}}{\rm{.}}\)
\( \Rightarrow {\rm{S}}{\rm{.P}}{\rm{.}} = 25000 – 5000\)
\( \Rightarrow {\rm{S}}{\rm{.P}}{\rm{.}} = 20000\)
Hence, Preethu must pay \({\rm{Rs}}{\rm{.}}\,20000\) to the shopkeeper for the television.

Q.3. In an automobile shop, a box of spare parts were sold for \({\rm{Rs}}{\rm{.}}\,1222,\) after the discount of \(6\% .\) Then, find the listed (marked) price of the box of spare parts.
Ans: Given selling price of the box of spare parts is \({\rm{Rs}}{\rm{.}}\,1222,\)
And, the discount percentage is given \(6\% .\)
We know that the discount percentage was given by the ratio of discount to the marked price, and that is multiplied by \(100.\)
Hence, the marked price of the product can be calculated as
\({\rm{M}}{\rm{.P}}. = \frac{{100 \times {\rm{S}}{\rm{.P}}.}}{{100 – \% \,{\rm{discount}}}}\)
\( \Rightarrow {\rm{M}}{\rm{.P}}. = 100 \times \frac{{1222}}{{100 – 6}}\)
\( \Rightarrow {\rm{M}}{\rm{.P}}. = 100 \times \frac{{1222}}{{94}}\)
\( \Rightarrow {\rm{M}}{\rm{.P}}. = 1300\)
Hence, the price listed on the box of spare parts is \({\rm{Rs}}.\,1300.\)

Q.4. On the eve of Diwali, a saree is sold for \({\rm{Rs}}.\,720\) after allowing \(20\,\% \) discount. What is the original price of the saree?
Ans: Given selling price of the saree is \({\rm{Rs}}.\,720.\)
And, the percentage of discount allowed on the saree is \(20\,\% .\)
We know that the discount percentage was given by the ratio of discount to the marked price, and that is multiplied by \(100.\)
Hence, the marked price of the product can be calculated as
\({\rm{M}}{\rm{.P}}. = \frac{{100 \times {\rm{S}}{\rm{.P}}.}}{{100 – \% \,{\rm{discount}}}}\)
\( \Rightarrow {\rm{M}}{\rm{.P}}{\rm{.}} = \frac{{100 \times {\rm{Rs}}{\rm{.}}\,720}}{{\left( {100 – 20} \right)}}\)
\( \Rightarrow {\rm{M}}{\rm{.P}}{\rm{.}} = 100 \times \frac{{720}}{{80}}\)
\( \Rightarrow {\rm{M}}{\rm{.P}}{\rm{.}} = 100 \times 9\)
\( \Rightarrow {\rm{M}}{\rm{.P}}{\rm{.}} = 900\)
Hence, the original price of the saree is \({\rm{Rs}}.\,900.\)

Q.5. The original price of the coffee in star bucks is \({\rm{Rs}}.\,50.\) And, it was sold for \({\rm{Rs}}.\,35\) after some discount. Find the rate of discount given?
Ans:
Given the original (marked) price of the coffee is \({\rm{Rs}}.\,50.\)
And, the selling price of the coffee is \({\rm{Rs}}.\,35.\)
We know that the discount percentage was given by the ratio of discount to the marked price, and that is multiplied by \(100.\)
\(\% \,{\rm{Discount}} = \frac{{{\rm{M}}{\rm{.P}}{\rm{.}} – {\rm{S}}{\rm{.P}}{\rm{.}}}}{{{\rm{M}}{\rm{.P}}{\rm{.}}}} \times 100\)
\( \Rightarrow \% \,{\rm{Discount}} = \frac{{{\rm{Rs}}{\rm{.}}\,50 – {\rm{Rs}}.\,35}}{{{\rm{Rs}}{\rm{.}}\,50}} \times 100\)
\( \Rightarrow \% \,{\rm{Discount}} = 15 \times 2 = 30\% \)
Hence, the rate of discount given on the coffee is \(30\% .\)

Summary

In this article, we have studied the definition of discounts, which tells the reduced price as compared to the listed price of the product. We have discussed the percentage discount with an example. We also studied the formulas of discount and percentage discount.

We have studied the different types of discounts like trade discounts, promotional discounts and quantity discounts. We also discussed the use of discounts. This article also gives the definitions of the marked or original price and selling price of the products. We discussed different types of solved examples on the discount, percentage discount, which help us understand the concept easily.

Frequently Asked Questions (FAQ) – Discounts:

Q.1. How do you define a discount?
Ans: Discount is the difference in price between the selling price of an object and the price listed on the object (marked price).

Q.2. What are the types of discounts?
Ans: There are three types of discounts
1. Trade Discounts
2. Quantity discounts
3. Promotional discounts

Q.3. How do I calculate a discount?
Ans: Discount can be calculated by finding the difference between the selling price and the marked price of the object.
\({\rm{Discount}} = {\rm{Marked}}\,{\rm{price}}\,\left( {{\rm{M}}{\rm{.P}}.} \right) – {\rm{Selling}}\,{\rm{price}}\,\left( {{\rm{S}}{\rm{.P}}{\rm{.}}} \right)\)

Q.4. How do I calculate discount percentage?
Ans: The discount percentage was given by the ratio of discount to the marked price, and that is multiplied by \(100.\)
\(\% \,{\rm{Discount}} = \frac{{{\rm{M}}{\rm{.P}}{\rm{.}} – {\rm{S}}{\rm{.P}}{\rm{.}}}}{{{\rm{M}}{\rm{.P}}{\rm{.}}}} \times 100\)

Q.5. What is the example of a discount?
Ans: Discounts can be offered in many ways. One of the ways is “Buy \(2\) Get \(1\)” in some shops to promote the sales of products is the best example of discounts.