👁 Preview — Study, Practice and Revise are open; mock tests and the rest of the syllabus unlock on subscription. Unlock all · ₹4,999
← Back to Basic Mathematics
Study mode

Discounts

Study Practice Revise 🔒 Test

Introduction to Discounts

Have you ever noticed a tag that says "10% off" or "Flat 20% discount" while shopping? These price reductions are what we call discounts. In everyday life, discounts help customers save money and encourage them to buy more items. Shops and sellers offer discounts to attract buyers, clear old stocks, or promote new products.

To understand discounts fully, it is important to know two key terms:

  • List Price (or Marked Price): This is the original price at which the item is displayed or marked before any discount.
  • Selling Price: This is the price the customer actually pays after the discount is applied.

The discount reduces the list price, and it is usually expressed as a percentage. For example, a 10% discount means the price is reduced by 10% of the list price - making the item cheaper to buy.

Understanding Discount and Percentage

Let's connect the concepts of list price, discount percent, discount amount, and selling price step by step.

The discount amount is the actual money deducted from the list price. The discount percent tells you how big this deduction is compared to the list price, expressed as a percentage.

Mathematically:

  • Discount Amount (D) is a part of the List Price (L).
  • The Selling Price (S) is what remains after discount: selling price = list price - discount amount.

This relationship is easy to visualize below:

Discount Amount (D) Selling Price (S) List Price (L)

In this rectangle, the total length represents the list price. The red part shows the discount amount, and the green part shows the selling price. This visualization helps us understand that the selling price plus discount amount equals the full list price.

Formulas for Discount Calculations

To calculate discount and selling price with percentages, the following formulas are very useful:

Discount Amount:
\[ D = \frac{p}{100} \times L \]

Selling Price:
\[ S = L - D \]

Or directly:
\[ S = L \times \left(1 - \frac{p}{100}\right) \]

Where:

  • \( D \) = Discount Amount (INR)
  • \( p \) = Discount Percent (%)
  • \( L \) = List Price or Marked Price (INR)
  • \( S \) = Selling Price after discount (INR)

These formulas form the foundation for all discount-related calculations.

Calculations Involving Discounts

Let's practice with an example to build comfort in calculating discount amounts and final prices.

Example 1: Single Discount Calculation Easy
Calculate the discount amount and selling price for an item priced at INR 2000 with a 10% discount.

Step 1: Identify the given values.

List Price, \( L = 2000 \) INR

Discount Percent, \( p = 10\% \)

Step 2: Calculate the discount amount using the formula:

\( D = \frac{p}{100} \times L = \frac{10}{100} \times 2000 = 200 \) INR

Step 3: Calculate the selling price:

\( S = L - D = 2000 - 200 = 1800 \) INR

Answer: Discount amount is INR 200 and the selling price is INR 1800.

Successive Discounts

Sometimes, a product might have two or more discounts given one after the other. These are called successive discounts. Instead of simply adding percentages, successive discounts compound - meaning the second discount is applied on the already discounted price after the first discount.

For example, if two successive discounts are 10% and 5%, the final selling price is calculated by multiplying the complements (100% - discount percentage) of each discount applied to the list price.

The formula for two successive discounts is:

Successive Discounts

\[Final\ Price = L \times \left(1 - \frac{p_1}{100}\right) \times \left(1 - \frac{p_2}{100}\right)\]

Calculate the price after applying two successive discounts

L = List price (INR)
\(p_1\) = First discount percent (%)
\(p_2\) = Second discount percent (%)
Example 2: Successive Discounts Medium
Find the final selling price if an item priced at INR 1500 is subjected to two successive discounts of 10% and 5%.

Step 1: Identify the given values.

List Price, \( L = 1500 \) INR

First discount, \( p_1 = 10\% \)

Second discount, \( p_2 = 5\% \)

Step 2: Calculate selling price after first discount:

\( S_1 = L \times \left(1 - \frac{10}{100}\right) = 1500 \times 0.90 = 1350 \) INR

Step 3: Apply second discount on \( S_1 \):

\( S = S_1 \times \left(1 - \frac{5}{100}\right) = 1350 \times 0.95 = 1282.50 \) INR

Answer: The final selling price after two successive discounts is INR 1282.50.

Finding Discount Percentage from Prices

Sometimes, you may know the list price and selling price and be asked to find the discount percentage given.

The formula is:

Discount Percentage from Prices

\[p = \left(\frac{L - S}{L}\right) \times 100\]

Calculate discount percent when list price and selling price are known

p = Discount percent (%)
L = List price (INR)
S = Selling price (INR)
Example 3: Finding Discount Percentage Medium
Determine the discount percent if the list price of an item is INR 2500 and the selling price is INR 2250.

Step 1: Identify given values.

List Price, \( L = 2500 \) INR

Selling Price, \( S = 2250 \) INR

Step 2: Calculate discount percent:

\( p = \left( \frac{2500 - 2250}{2500} \right) \times 100 = \frac{250}{2500} \times 100 = 10\% \)

Answer: The discount percent is 10%.

Formula Bank

Formula Bank

Discount Amount
\[ D = \frac{p}{100} \times L \]
where: \( D \) = discount amount (INR), \( p \) = discount percent (%), \( L \) = list price (INR)
Selling Price (using Discount Amount)
\[ S = L - D \]
where: \( S \) = selling price (INR), \( L \) = list price (INR), \( D \) = discount amount (INR)
Selling Price (direct using percent)
\[ S = L \times \left(1 - \frac{p}{100}\right) \]
where: \( S \) = selling price (INR), \( L \) = list price (INR), \( p \) = discount percent (%)
Successive Discounts
\[ \text{Final Price} = L \times \left(1 - \frac{p_1}{100}\right) \times \left(1 - \frac{p_2}{100}\right) \]
where: \( L \) = list price (INR), \( p_1 \) = first discount percent (%), \( p_2 \) = second discount percent (%)
Discount Percentage from Prices
\[ p = \left( \frac{L - S}{L} \right) \times 100 \]
where: \( p \) = discount percent (%), \( L \) = list price (INR), \( S \) = selling price (INR)
Example 4: Real-life Shopping Scenario Easy
A catalogue lists a washing machine for INR 12,000 with a discount of 15%. Calculate the amount to be paid by the customer.

Step 1: Given values:

List Price, \( L = 12000 \) INR

Discount Percent, \( p = 15\% \)

Step 2: Calculate discount amount:

\( D = \frac{15}{100} \times 12000 = 1800 \) INR

Step 3: Calculate final amount to pay:

\( S = L - D = 12000 - 1800 = 10200 \) INR

Answer: The customer will pay INR 10,200 for the washing machine.

Example 5: Comparing Discounts Hard
An item costs INR 10,000. Which offer is better? A 20% discount on the marked price or two successive discounts of 10% and 12%?

Step 1: Calculate final price with 20% single discount:

\( S_1 = 10000 \times \left(1 - \frac{20}{100}\right) = 10000 \times 0.80 = 8000 \) INR

Step 2: Calculate final price with successive discounts of 10% and 12%:

\( S_2 = 10000 \times \left(1 - \frac{10}{100}\right) \times \left(1 - \frac{12}{100}\right) \)

\(= 10000 \times 0.90 \times 0.88 = 10000 \times 0.792 = 7920 \) INR

Step 3: Compare \( S_1 \) and \( S_2 \):

\( S_1 = 8000 \) INR,
\( S_2 = 7920 \) INR

The option with successive discounts leads to a lower price, so it is the better offer.

Answer: Successive discounts of 10% and 12% provide a better deal with a final price of INR 7920.

Tips & Tricks

Tip: Convert percentage discount directly into a decimal multiplier to find the selling price quickly, e.g., 10% discount means multiply by 0.90.

When to use: Speed calculation of discounted price without calculating discount amount separately.

Tip: For successive discounts, multiply the complements of discount percentages instead of subtracting sequentially. For example, use (1 - p1/100) x (1 - p2/100).

When to use: Avoid repeated subtraction errors and save time during calculations.

Tip: To find discount percent from prices, use proportion if you forget formulas: Discount / List Price = p / 100.

When to use: When formulas don't come to mind immediately.

Tip: Use estimation to quickly check if your discount calculations seem reasonable before finalizing.

When to use: Quickly verify answers in exam settings to avoid silly mistakes.

Tip: For multiple-choice questions, discard unrealistic prices or discount amounts first to save calculation time.

When to use: When answer choices vary widely and quick elimination is possible.

Common Mistakes to Avoid

❌ Calculating discount percentage as (Selling Price / List Price) x 100 instead of ((List Price - Selling Price) / List Price) x 100.
✓ Remember discount percent measures price reduction, so subtract selling price from list price before dividing.
Why: Confusing the definition of discount percent with selling price as a percentage leads to incorrect answers.
❌ Adding successive discount percentages directly instead of multiplying their complements.
✓ Use the successive discount formula: multiply (1 - p/100) terms instead of adding percentages.
Why: Successive discounts compound and cannot just be summed.
❌ Ignoring currency units or mixing units like INR with other currencies, leading to confusion in answers.
✓ Always include INR and clearly state prices especially in word problems.
Why: Mixing units causes misinterpretation and answer errors.
❌ Confusing discount amount with selling price.
✓ Keep in mind that selling price = list price - discount amount.
Why: Terminology confusion can mistakenly swap these values, causing errors.
❌ Applying discount on selling price instead of list price for single discounts.
✓ Apply discount percentage only on list price unless successive discounts are specified.
Why: Wrong base for discount calculation leads to incorrect selling price.
Curated videos per subtopic
Top YouTube explainers, AI-ranked for your exam and language. Unlocks with subscription.
Unlock

Try Practice next.

Progress tracking is paywalled — subscribe to mark subtopics as understood and save your streak.

Go to practice →
Ask a doubt
Discounts · 10 free messages
Ask me anything about this subtopic. You have 10 free messages this session — chat history isn't saved in preview.