Class 8 - Discount

Shops and online shopping websites sometimes sell their products at a lower price. This reduction in price is called a discount. The original price printed is called the marked price (MP). The amount reduced is called the discount. Discount is always calculated on the MP of the article. The price of the item after the reduction of the discount is called the selling price (SP).

• Discount = marked price − selling price

Table of Contents

• What Is a Discount?
• Discount Formula
• Solved Examples On Discount
• Practice Questions On Discount

What Is a Discount?

When a shopkeeper reduces the price of a product from what is written on the price tag, that reduction is called a discount. Every day we see boards that say "flat 20% off" or "buy one get one free"  all of these are forms of discount. There are three terms you need to keep in mind before learning the formulas. The Marked Price is the price that is printed or written on the product by the seller. It is also called the List Price. This is the price before any reduction. The Selling Price is the actual amount the buyer pays after the discount is applied. It is always less than or equal to the marked price. The Discount is simply the difference between the marked price and the selling price. It is the amount the seller agrees to give up.

Discount Formula

• Discount = Marked Price − Selling Price
• Discount% = (Discount / Marked Price) × 100
• Selling Price = Marked Price − Discount
• SP = MP × (1 − Discount%/100)

Successive Discount

Sometimes a seller offers two or more discounts one after the other. For example, a store might say "first 30% off, and then an additional 10% off on the new price." This is called a successive discount or a series of discounts.

The important thing to understand is that the second discount is not applied on the original marked price. It is applied on the price that remains after the first discount is already taken. This is what makes successive discounts different from a single flat discount.

Net Discount %=a+b−ab100

Where a and b are the two discount percentages.

Solved Examples On Discount

Example 1: Finding Discount and SP

Problem: A bag has MRP Rs. 800 and is offered at 15% discount. Find the discount and selling price.

Solution:

• Discount = 15% of 800 = (15/100) × 800 = Rs. 120

• SP = 800 − 120 = Rs. 680

Answer: Discount = Rs. 120, SP = Rs. 680.

Example 2: Finding Discount Percentage

Problem: MP = Rs. 600, SP = Rs. 480. Find the discount%.

Solution:

• Discount = 600 − 480 = Rs. 120

• Discount% = (120/600) × 100 = 20%

Answer: Discount = 20%.

Example 3: Finding Marked Price

Problem: After a 25% discount, the selling price of a dress is Rs. 1500. Find the marked price.

Solution:

• SP = MP × (1 − 25/100) = MP × 0.75

• 1500 = MP × 0.75

• MP = 1500 / 0.75 = Rs. 2000

Answer: MP = Rs. 2000.

Example 4: Successive Discounts

Problem: MP = Rs. 1000. First discount 20%, then additional 10%. Find final SP.

Solution:

• After first discount: SP₁ = 1000 × (1 − 0.20) = Rs. 800

• After second discount: SP₂ = 800 × (1 − 0.10) = Rs. 720

Answer: Final SP = Rs. 720. (Note: this is NOT the same as 30% off.)

Example 5: Comparing Discounts

Problem: Shop A: MP Rs. 500, discount 20%. Shop B: MP Rs. 550, discount 25%. Which is cheaper?

Solution:

• Shop A: SP = 500 × 0.80 = Rs. 400

• Shop B: SP = 550 × 0.75 = Rs. 412.50

Answer: Shop A is cheaper by Rs. 12.50.

Practice Questions On Discount

1. A jacket is marked at one thousand five hundred rupees. A discount of twelve percent is given. Find the selling price. (Answer: ₹1,320)

2. A mobile phone is sold for eight thousand four hundred rupees at a discount of sixteen percent. What is its marked price? (Answer: ₹10,000)

3. Two successive discounts of twenty-five percent and twenty percent are offered on a sofa marked at twelve thousand rupees. Find the final selling price and the equivalent single discount percentage. (Answer: Equivalent discount is 40%, Final selling price is ₹7,200)

4. A shopkeeper marks his goods forty percent above the cost price and then gives a discount of twenty percent. Find the profit or loss percentage. (Answer: Profit of 12%)

5. A product with a marked price of five thousand rupees is given three successive discounts of ten percent, ten percent, and ten percent. Find the final selling price. (Answer: ₹3,645)