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In malls and shops, we come to see many items offered by shop owners. In order to increase the sale of goods, shop owners offer discounts to customers. The rebate or the offer given to the customers on the marked price of products is termed known as a discount.

Let’s understand what a discount is and how to calculate percentage discount.

## Discount Related Terms

Many items in a shop are sold by the shop owners at a price lower than the price marked on them. The difference in price is called a discount. There are various terms that are associated with discounts, such as cost price(C.P.), selling price (S.P.), discount, and marked price(or list price). First, let’s start to understand these terms.

**Cost Price(C.P.):** The price at which an article is bought is called its cost price. For example, if a person buys a notebook for ₹$25$, this is called the cost price of the notebook and is abbreviated as C.P.

**Selling Price(S.P.):** The price at which an article is sold is called its selling price. For example, if a person sells the same notebook for ₹$30$, this is called the selling price of the notebook and is abbreviated as S.P.

**Marked Price:** Marked price is the price set by the seller on the label of the article. It is a price at which the seller offers a discount. After the discount is applied to the marked price, it is sold at a reduced price known as the selling price.

For example, you go to a shop and purchase a dress. The price tag on the dress is ₹$1,500$. This means the marked price(or list price) of the dress is ₹$1,500$.

## What is Discount?

Discount is the reduction in the price of goods or services offered by shop owners at the marked price. This percentage of the rebate is usually offered to increase sales or clear the old stock of goods.

The list price or marked price is the price of an article as declared by the seller or the manufacturer, without any reduction in price. The selling price is the actual price at which an article is sold after any reduction or discounts in the list price.

The commonly used terms for discounts are “Off”, and “Reduction”.

### How to Calculate Discount?

The formula to calculate discount is:

The steps involved in calculating discounts are:

**Step 1:** Identify the values of the list price and the final selling price of an item

**Step 2**: Find the value of the discount amount by subtracting the selling price from the list price

### Examples

**Ex 1:** You go to a shop and purchase a dress. The price tag on the dress is ₹$1,500$ and if the shopowner offers to sell the dress for ₹$1,200$.

Here, the list price(L.P.) or marked price(M.P.) = ₹$1,500$.

And, the selling price(S.P.) = ₹$1,200$.

According to the formula $\text{Discount} = \text{M.P./L.P.} – \text{S.P.} = 1,500 – 1,200 =$₹$300$.

Therefore, the discount on the dress is $1,500 – 1,200 =$₹$300$.

**Ex 2**: Let us consider one more example to understand the procedure behind calculating discounts and sales prices.

Think of a pair of shoes you wish to buy. Now you might want to calculate the sales price which is regularly ₹$2,500$ if the shoes are ₹$500$ off.

Here, you have the list price(L.P.) or marked price(M.P.) = ₹$2,500$.

And, the discount = ₹$500$.

According to the formula $\text{Discount} = \text{M.P./L.P.} – \text{S.P.} =>\text{S.P.} = \text{M.P./L.P.} – \text{Discount} = 2,500 – 500 =$₹$2,000$.

Therefore, the final selling price of a pair of shoes is ₹$2,000$.

### How to Calculate Percentage Discount?

Let’s now learn how to calculate percentage discount. The formula to calculate percentage discount or discount percentage is:

The steps involved in calculating discounts are:

**Step 1:** Identify the values of the list price and the final selling price of an item

**Step 2**: Find the value of the discount amount by subtracting the selling price from the list price

**Step 3:** Divide the discount amount by the list price, and then multiply it by $100$

### Examples

**Ex 1:** You go to a shop and purchase a pair of trousers. The price tag on the dress is ₹$3,500$ and if the shopowner offers to sell the dress for ₹$2,800$.

Here, the list price(L.P.) or marked price(M.P.) = ₹$3,500$.

And, the selling price(S.P.) = ₹$2,800$.

$\text{Discount} = \text{M.P./L.P.} – \text{S.P.} = 3,500 – 2,800 =$₹$700$.

And then using the discount percentage formula, we get $\text{Discount}\% = \frac {\text{Discount}}{\text{M.P./L.P.}} \times 100 = \frac{700}{3,500} \times 100 = 20\%$.

Therefore, the discount percentage on the pair of trousers is $20\%$.

**Ex 2:** Let us consider one more example to understand the procedure behind calculating discount percentages and sales prices.

Think of a pair of shoes you wish to buy. Now you might want to calculate the sales price which is regularly ₹$2,500$ if the shoes are $15\%$ off.

Here, $\text{M.P./L.P.} =$₹$2,500$.

And, $\text{Discount} \% = 15\%$.

$\text{Discount} = \frac{\text{Discount} \% \times \text{L.P.}}{100} = \frac{15 \times 2,500}{100} = $₹$375$

And now, $\text{S.P.} = \text{L.P.} – \text{Discount} = 2,500 – 375 =$₹$2,125$.

**Note:** Discount is always calculated on the Marked price (List price) of the article.

## Conclusion

A discount is a reduction in the price of goods or services offered by shop owners at the marked price and the discount percentage is always calculated on the marked price or list price of an item.

## Practice Problems

- A bicycle marked at ₹$2,500$ is sold for ₹$2,200$. What is the percentage of the discount?
- An almirah is sold at ₹$5,520$ after allowing a discount of $8\%$. Find its marked price.
- The marked price of a table is Rs 1200. It is sold at Rs. 1056 after allowing a certain discount. Find the discount percentage.
- A shop owner offers a discount of $20\%$ on all the items at his shop and still makes a profit of $12\%$. What is the cost price of an article marked at ₹$280$?
- A trader marks his goods at $50\%$ above the cost price and allows a discount of $30\%$. What is his gain percent?

## Recommended Reading

- Profit & Loss(Meaning, Formulas & Examples)
- What is Unitary Method? (Meaning, Formula & Examples)
- What is Percentage – Meaning, Formula & Examples
- What is Proportion? (With Meaning & Examples)
- What is Ratio(Meaning, Simplification & Examples)
- Factors and Multiples (With Methods & Examples)
- Fractions On Number Line – Representation & Examples
- Reducing Fractions – Lowest Form of A Fraction
- Comparing Fractions (With Methods & Examples)
- Like and Unlike Fractions
- Improper Fractions(Definition, Conversions & Examples)
- How To Find Equivalent Fractions? (With Examples)
- 6 Types of Fractions (With Definition, Examples & Uses)
- What is Fraction? – Definition, Examples & Types
- Mixed Fractions – Definition & Operations (With Examples)
- Multiplication and Division of Fractions
- Addition and Subtraction of Fractions (With Pictures)

## FAQs

### What is meant by discount?

Discount is the reduction in the price of goods or services offered by shop owners at the marked price. This percentage of the rebate is usually offered to increase sales or clear the old stock of goods.

### How discount is calculated?

The formula to calculate discount is $\text{Discount} = \text{Marked Price/List Price} – \text{Selling Price}$.

### How discount percentage is calculated?

The formula for calculating the discount percentage = $\frac{\text{Discount}}{\text{L.P.}} \times 100$.

where L.P. is the List Price

Discount = L.P. – S.P., where S.P. is the selling price