Discount Formula in Maths: Marked Price vs Selling Price

In everyday life, a discount simply means a reduction in the price of a product or service. Imagine you walk into a store and see a shirt with a price tag of $1000. If the store announces a 20% discount, you’ll pay less than the marked price—$800 instead of $1000. That difference of $200 is the discount. Discounts are everywhere: seasonal sales, clearance offers, festive promotions, and even online shopping deals. They make shopping more attractive while helping businesses sell more.

Discount Formula in Maths

The discount formula is a fundamental concept in mathematics that connects the marked price, selling price, and the discount offered. It is widely used in both academic contexts (percentage problems, profit & loss) and real-world scenarios (shopping, business pricing strategies).

Basic Discount Formula

The most straightforward way to express discount is:

$$\text{Discount}=\text{Marked Price}-\text{Selling Price}$$

• Marked Price (MP): The listed price before any reduction.
• Selling Price (SP): The actual price paid after discount.
• Discount: The difference between MP and SP.

Example: If a laptop has a marked price of $1200 and is sold for $960, then:

$$\text{Discount}=1200-960=\mathrm{\$}240$$

Discount Percentage Formula

To understand the discount in relative terms, we calculate the percentage:

$$\text{Discount Percentage}=\frac{\text{Discount}}{\text{Marked Price}}\times 100$$

Example: Using the laptop example above:

$$\text{Discount Percentage}=\frac{240}{1200}\times 100=20\mathrm{\%}$$

This shows the buyer received a 20% discount.

Selling Price Formula After Discount

Instead of calculating discount first, you can directly find the selling price using:

$$\text{Selling Price}=\text{Marked Price}\times (1-\frac{\text{Discount \%}}{100})$$

Example: Marked Price = $1200, Discount = 20%

$$SP=1200\times (1-\frac{20}{100})=1200\times 0.8=\mathrm{\$}960$$

This shortcut is especially useful in exams and quick shopping calculations.$$\text{Discount Percentage}=\frac{\text{Discount}}{\text{Marked Price}}\times 100$$

What Is Marked Price (MP) and Selling Price (SP)?

Definition of Marked Price (List Price)

The Marked Price (MP), sometimes called the list price or Maximum Retail Price (MRP), is the price printed on the product before any discount is applied. It represents the seller’s intended value of the item and is usually displayed on tags, packaging, or product listings. In retail, the marked price is often set higher than the actual selling price to allow room for promotional discounts and offers.

Definition of Selling Price (Actual Price Paid)

The Selling Price (SP) is the actual amount the customer pays after discounts or reductions are applied. It reflects the final transaction value. Selling price is always less than or equal to the marked price, depending on whether a discount is offered.

Mathematically:

$$SP=MP-\text{Discount}$$

Watch Video Explanation

Real-Life Examples (MRP vs Discounted Price in Stores)

• Clothing Store Example: A shirt has an MRP of $1500. During a festival sale, the store offers a 20% discount. The selling price becomes $1200.
• Electronics Example: A smartphone is marked at $2,000. An online platform offers a flat $300 discount, so the selling price is ₹1,700.
• Supermarket Example: A packet of biscuits has an MRP of $50. The store runs a “Buy 2, Get 1 Free” offer. Effectively, the selling price per packet drops to around $33.

These examples show how marked price is the reference point, while selling price is the actual cost to the buyer.

Takeaway:

The difference between them is the discount, which is central to understanding the discount formula in maths and commerce.

Marked Price = the listed or printed price.

Selling Price = the final price after discounts.

Example: Discount Formula in Action

• Marked Price (MP): $5000
• Discount: 20%

Step 1: Calculate the Discount Amount

$$\text{Discount Amount}=\frac{20}{100}\times 5000=\mathrm{\$}1000$$

Step 2: Find the Selling Price (SP)

$$SP=MP-\text{Discount}=5000-1000=\mathrm{\$}4000$$

Final Result

The savings (discount) are $1000.

The customer pays $4000.

Comparisons and Data Illustration

Scenario	Marked Price	Discount %	Selling Price	Savings
Jacket A	$2000	20%	$1600	$400
Jacket B	$2500	30%	$1750	$750
Jacket C	$3000	10%	$2700	$300

From the table, Jacket B offers the highest savings, but Jacket A may still be cheaper overall.

Advanced Angle: Successive Discounts

Sometimes, stores apply multiple discounts (e.g., 20% off, then an extra 10%). The formula adapts:

$$\text{Final Price}=MP\times (1-\frac{d1}{100})\times (1-\frac{d2}{100})$$

This shows why successive discounts are not simply additive.

Practical Tips for Using the Discount Formula

The discount formula is simple in theory, but applying it correctly in real-life situations requires attention to detail. Here are some practical tips to make sure you use it effectively both in academics and everyday shopping.

Always Check If the Discount Is on the Marked Price or on a Reduced Price

• Discounts can be applied directly on the Marked Price (MP) or on a reduced price after a first discount (successive discounts).
• Example:
  • MP = $1000
  • First discount = 20% → SP = $800
  • Second discount = 10% → SP = $800 × 0.9 = $720
  • Effective discount = 28%, not 30%.
• Tip: Always confirm whether the discount is applied once or successively to avoid miscalculations.

Compare Selling Prices Across Stores, Not Just Discount Percentages

• A higher discount percentage doesn’t always mean a better deal.
• Example:
  • Store A: MP = $200, Discount = 30% → SP = $140
  • Store B: MP = $180, Discount = 20% → SP = $144
  • Even though Store A offers a bigger discount, Store B’s selling price is lower.
• Tip: Focus on the final selling price, not just the advertised discount percentage.

Use the Formula to Verify If Promotional Offers Are Genuinely Beneficial

• Retailers often inflate marked prices before applying discounts.
• Example: A product marked at $100 is sold at $80 after a “20% discount.” But if the actual market value is $85, the discount is less impressive.
• Tip: Use the formula to calculate the real savings and compare with market value to judge if the offer is truly beneficial.

Track Long-Term Spending by Calculating Total Discounts Received

• Keeping track of discounts helps you understand your savings habits.
• Example:
  • January: Saved $50 on groceries
  • February: Saved $120 on electronics
  • March: Saved $80 on clothing
  • Total savings in 3 months = $250
• Tip: Recording discounts over time helps with budgeting and shows how much value you gain from shopping smart.

Common Mistakes Students Make

Even though the discount formula is straightforward, students often make avoidable errors when applying it in maths problems or real-life scenarios. Recognizing these mistakes helps build accuracy and confidence.

Using SP Instead of MP in Discount % Formula

• Mistake: Students sometimes calculate discount percentage using the Selling Price (SP) instead of the Marked Price (MP).
• Correct Formula:

$$\text{Discount \%}=\frac{\text{Discount}}{\text{Marked Price}}\times 100$$

• Example Error: MP = $500, SP = $400, Discount = $100 Wrong: $\frac{100}{400}\times 100=25\mathrm{\%}$ Correct: $\frac{100}{500}\times 100=20\mathrm{\%}$

Confusing Discount with Profit

• Mistake: Students mix up discount (reduction from marked price) with profit (gain over cost price).
• Key Difference:
  • Discount is based on Marked Price (MP).
  • Profit is based on Cost Price (CP).
• Example: A shopkeeper buys a pen for $10 (CP), marks it at $20 (MP), and sells it at $15 (SP).
  • Discount = $20 – $15 = $5
  • Profit = $15 – $10 = $5 Both values are equal here, but conceptually they are different.

Calculation Errors with Percentages

• Mistake: Students often misapply percentage calculations, especially with successive discounts or fractional percentages.
• Example Error: MP = $1000, Discount = 25% Wrong: $1000 – 25 = $975 (incorrect subtraction of percentage as a number). Correct: $1000\times (1-\frac{25}{100})=1000\times 0.75=\mathrm{\$}750$.
• Successive Discount Trap: A 20% discount followed by 10% is not equal to 30%. Correct Calculation:

$$SP=MP\times (1-0.20)\times (1-0.10)$$

$$SP=1000\times 0.8\times 0.9=\mathrm{\$}720$$

Effective discount = 28%, not 30%.

Conclusion

The discount formula is more than a classroom exercise—it’s a financial tool that helps consumers, businesses, and students alike. By understanding the relationship between marked price and selling price, one can make smarter decisions, whether in exams or in everyday shopping. For deeper financial analysis, the discount formula also connects to broader concepts like profit margins, pricing strategies, and consumer psychology.

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