Discount and Markup Formulas with Solved Examples
Understanding the Discounts and Markups Formula is essential in arithmetic and commercial mathematics. These concepts are frequently tested in school and competitive exams, and are widely used in real-life scenarios such as shopping, business transactions, and budgeting. Mastering this topic will help you solve percentage and profit-loss problems quickly and accurately.
What are Discounts and Markups?
A discount is a reduction in the price of an item, usually offered to attract buyers or clear stock. On the other hand, a markup is the amount added to the cost price of an item by a seller to determine its selling price and earn a profit. Both these operations are based on percentages and are key skills for solving various arithmetic and commercial math questions.
Key Terms and Definitions
| Term | Definition | Example |
|---|---|---|
| Cost Price (CP) | The price at which an item is purchased by a seller. | Shopkeeper buys a shirt at ₹400 (CP = 400) |
| Marked Price (MP) / List Price (LP) | The price marked on the article, before any discounts. | MP for the shirt is ₹500 |
| Selling Price (SP) | The final price paid by the buyer after discounts. | After discount, shirt sold at ₹450 (SP = 450) |
| Discount | Difference between Marked Price and Selling Price. | ₹500 - ₹450 = ₹50 |
| Markup | Difference between Marked Price and Cost Price. | ₹500 - ₹400 = ₹100 |
Discounts and Markups Formulae
Here are the main formulas for calculating discounts and markups:
- Discount = Marked Price - Selling Price
- Discount Percentage = (Discount / Marked Price) × 100
- Markup = Marked Price - Cost Price
- Markup Percentage = (Markup / Cost Price) × 100
These formulas help you find the discount amount, percentage of discount, the markup amount, and markup percent, making problem-solving systematic.
For example, if a bag has a marked price of ₹600 and is sold at ₹540, then:
- Discount = ₹600 - ₹540 = ₹60
- Discount % = (60/600) × 100 = 10%
Worked Examples
Let’s see how to use these formulas in various scenarios:
Example 1: Finding Discount and Selling Price
- A television has a marked price of ₹25,000. If a shopkeeper offers a 12% discount, what is the selling price?
- Discount = 12% of ₹25,000 = (12/100) × 25,000 = ₹3,000
- Selling Price = Marked Price - Discount = ₹25,000 - ₹3,000 = ₹22,000
Example 2: Calculating Markup and Markup Percentage
- A retailer buys a jacket for ₹800 and marks it at ₹1,000. Find the markup amount and markup percentage.
- Markup = ₹1,000 - ₹800 = ₹200
- Markup % = (200/800) × 100 = 25%
Example 3: Combined Discount and Markup
- Cost Price of an item = ₹350, Marked Price = ₹420, Discount = 10%. Find the final selling price.
- Discount = 10% of ₹420 = ₹42
- Selling Price = Marked Price - Discount = ₹420 - ₹42 = ₹378
- Markup = ₹420 - ₹350 = ₹70; Markup % = (70/350) × 100 = 20%
Practice Problems
- A watch is marked at ₹2,500. If it is sold for ₹2,000, what is the discount percentage?
- If the cost price of a shirt is ₹300, it's marked at ₹390, and sold for ₹370, find the markup percentage and discount percentage.
- A laptop is bought for ₹40,000 and sold at a markup of 10%. What is the selling price before any discount?
- If an article is offered at a 25% discount on the marked price of ₹240, what is the selling price?
- An item is marked at ₹600. A shopkeeper offers two successive discounts of 10% and 5%. What is the final selling price?
Common Mistakes to Avoid
- Confusing the base for percentage calculations (discount is always on Marked Price, markup is always on Cost Price).
- Not applying successive discounts correctly (second discount is on the already reduced price).
- Mixing up formulas for markup and discount.
- Forgetting to subtract discount from marked price to get selling price.
Real-World Applications
Discounts and markups are used every day in shopping, retail, and business. When you see a “SALE 20% OFF” sign in a store, the reduction is calculated using the discount formula. Businesses set the selling price of goods by adding a markup to the cost price to make a profit. Understanding these calculations helps you budget better, shop smartly, and succeed in commerce-related careers.
In this topic, we learned the importance of the Discounts and Markups Formula in pricing, shopping, and business. You can now confidently solve related questions in school, competitive exams, and use these calculations in real-life. For more practice and to explore commercial math topics further, visit other resources at Vedantu like Discount Rate and Application of Percentage.
FAQs on How to Calculate Discounts and Markups in Maths
1. What is the formula for discount and markup?
The discount formula calculates the difference between the marked price and the selling price: Discount = Marked Price - Selling Price. The markup formula calculates the difference between the selling price and the cost price: Markup = Selling Price - Cost Price. Both formulas also have percentage-based versions.
2. What is the formula for marked up price and discount?
To find the marked-up price, add the markup to the cost price: Marked-up Price = Cost Price + Markup. The discount is calculated by subtracting the discount amount from the marked price: Selling Price = Marked Price - Discount. Remember to use percentage formulas when dealing with discount rates or markup percentages.
3. What is the formula for markup?
The markup formula is: Markup = Selling Price - Cost Price. This shows how much extra a business adds to the cost to determine the selling price. The markup percentage is calculated as: Markup % = (Markup / Cost Price) × 100.
4. What is a discount formula?
The basic discount formula is: Discount = Marked Price - Selling Price. This shows the amount of reduction in price. The discount percentage is calculated as: Discount % = (Discount / Marked Price) × 100. Understanding both is crucial for commercial mathematics problems.
5. What is the discount percentage formula?
The discount percentage formula is: Discount % = (Discount / Marked Price) × 100. This helps determine the rate of reduction offered on the original marked price. Remember that the discount is the difference between the marked price and the selling price.
6. How do you calculate selling price after discount?
The selling price after a discount is calculated by subtracting the discount amount from the marked price: Selling Price = Marked Price - Discount. Alternatively, you can calculate it using the discount percentage: Selling Price = Marked Price × (1 - Discount Percentage).
7. What is the Markup Percentage formula?
The markup percentage formula is: Markup % = (Markup / Cost Price) × 100. This shows the percentage increase added to the cost price to arrive at the selling price. It's a key concept in understanding business profit margins.
8. How to calculate discounts and markups?
Calculating discounts and markups involves using simple formulas based on cost price, marked price, and selling price. For discounts, subtract the discount from the marked price to find the selling price. For markups, add the markup to the cost price to find the selling price. Remember to use percentage versions of the formulas when working with rates.
9. Where are discounts and markups used in real life?
Discounts and markups are used extensively in everyday life, especially in retail settings. Businesses use markups to set prices that ensure a profit. Discounts are used to attract customers and clear stock. You encounter both when shopping, dealing with sales, and even in business calculations.
10. Formula of discount Class 8?
The discount formula relevant for Class 8 is: Discount = Marked Price - Selling Price. The discount percentage is: Discount % = (Discount / Marked Price) × 100. These formulas are foundational to understanding commercial mathematics concepts within the Class 8 syllabus.
11. Can an item have both a markup and a discount applied sequentially?
Yes, an item can have both a markup and a discount applied sequentially. Businesses might first mark up the cost to determine the selling price and then offer a discount on this selling price, especially during sales events. The order of operations is important in determining the final selling price.
12. How do taxes affect the final selling price after applying discount and markup?
Taxes like GST or VAT are usually added to the selling price *after* any discounts have been applied. However, the specific order of applying taxes, markups, and discounts can vary depending on the country or region's tax laws and business practices. Therefore, it is important to check the specific rules for the location in question.
