How to Calculate Discount and Markup Using Formula 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 Discounts and Markups Formula with Examples and Steps
1. What is the discount formula in maths?
The discount formula is Discount = Marked Price × (Discount % / 100).
- Discount is the reduction given on the marked price.
- Marked Price (MP) is the original listed price.
- Selling Price (SP) after discount = MP − Discount.
2. What is the markup formula?
The markup formula is Markup = Cost Price × (Markup % / 100).
- Cost Price (CP) is the original cost of the item.
- Marked Price (MP) = CP + Markup.
3. How do you calculate selling price after a discount?
The selling price after discount is calculated using SP = Marked Price − Discount.
- First find Discount = MP × (Discount % / 100).
- Then subtract it from MP.
4. What is the formula for discount percentage?
The discount percentage formula is Discount % = (Discount / Marked Price) × 100.
- Find the discount amount.
- Divide it by the marked price.
- Multiply by 100.
5. What is the formula for markup percentage?
The markup percentage formula is Markup % = (Markup / Cost Price) × 100.
- Find the markup amount.
- Divide by cost price.
- Multiply by 100.
6. What is the difference between discount and markup?
The difference between discount and markup is that discount reduces the marked price, while markup increases the cost price.
- Discount is subtracted from the marked price to get selling price.
- Markup is added to the cost price to get marked price.
- Discount is usually given to customers; markup is added by sellers for profit.
7. How do you calculate marked price?
The marked price is calculated using MP = Cost Price + Markup.
- First calculate Markup = CP × (Markup % / 100).
- Add markup to cost price.
8. How do you calculate profit after discount?
The profit after discount is calculated as Profit = Selling Price − Cost Price.
- First find SP after discount.
- Then subtract CP from SP.
9. What is successive discount formula?
The successive discount formula is Net Discount % = a + b − (ab/100) for two discounts a% and b%.
- This formula combines two discounts applied one after another.
- It avoids calculating step by step.
10. Can you give a simple example of discount and markup calculation?
A simple example of markup and discount calculation involves finding marked price first and then applying discount.
- CP = 500, Markup = 20% → Markup = 500 × 20/100 = 100.
- MP = 500 + 100 = 600.
- Discount = 10% on MP → 600 × 10/100 = 60.
- SP = 600 − 60 = 540.
