Discount Calculation
When you shop during a sale, prices are reduced. The amount by which the price is reduced is called a discount. Shops offer discounts as a percentage of the marked price (MRP or list price).
The price you actually pay after the discount is the selling price. If a shirt has MRP Rs. 500 and a 20% discount, you save Rs. 100 and pay Rs. 400.
Understanding discounts helps you calculate savings and compare deals when shopping.
What is Discount Calculation - Grade 7 Maths (Comparing Quantities)?
Definition:
- Marked Price (MP): The original price printed on the product (also called MRP or list price).
- Discount: The reduction given on the marked price.
- Selling Price (SP): The price actually paid by the customer after discount.
- Discount Percentage: The discount expressed as a percentage of the marked price.
Discount Calculation Formula
Formulas:
Discount = Marked Price − Selling Price
Discount% = (Discount / Marked Price) × 100
Selling Price = Marked Price − Discount
Or equivalently:
SP = MP × (1 − Discount%/100)
Types and Properties
Types of Discount Problems:
- Finding discount amount: Given MP and discount%, find the discount.
- Finding selling price: Given MP and discount%, find SP.
- Finding discount percentage: Given MP and SP, find discount%.
- Finding marked price: Given SP and discount%, find MP.
- Successive discounts: Two or more discounts applied one after another.
Solved Examples
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.
Example 6: Word Problem — Sale
Problem: During a sale, a jacket marked Rs. 2400 is sold at Rs. 1800. Find the discount%.
Solution:
- Discount = 2400 − 1800 = Rs. 600
- Discount% = (600/2400) × 100 = 25%
Answer: Discount = 25%.
Real-World Applications
Real-world uses:
- Shopping: Calculating savings during sales and festivals.
- Comparing deals: Finding which shop offers the better price.
- Business: Shops decide discount% to attract customers while maintaining profit.
- Online shopping: Coupons and promotional codes give percentage discounts.
Key Points to Remember
- Discount = Marked Price − Selling Price.
- Discount% = (Discount / MP) × 100.
- SP = MP × (1 − Discount%/100).
- Successive discounts of a% and b% are NOT equal to (a + b)%.
- The marked price is always the starting point for calculating discount.
- Discount is always calculated on the MP, not on the SP.
Practice Problems
- MP = Rs. 1200, discount = 30%. Find SP.
- SP = Rs. 450, discount = 10%. Find MP.
- MP = Rs. 750, SP = Rs. 600. Find discount%.
- Successive discounts of 15% and 10% on Rs. 2000. Find final SP.
- Which is better: a single discount of 30% or successive discounts of 20% and 10%?
Frequently Asked Questions
Q1. What is a discount?
A discount is the amount by which the marked price is reduced. It is usually given as a percentage of the marked price.
Q2. What is the difference between MP and SP?
MP (Marked Price) is the original/listed price. SP (Selling Price) is the price after discount. SP = MP − Discount.
Q3. Are two successive discounts of 10% the same as 20% off?
No. Two successive 10% discounts give SP = MP × 0.9 × 0.9 = 0.81 × MP, which is 19% off. A single 20% gives 0.80 × MP. So successive discounts give slightly less total discount.
Q4. Can discount be more than 100%?
No. A 100% discount means the item is free. Discount cannot exceed the marked price.
Related Topics
- Profit and Loss
- Introduction to Percentage
- Simple Interest
- Percentage Increase and Decrease
- Compound Interest
- Applications of Compound Interest
- Sales Tax and VAT
- Growth and Decay
- Finding Percentage of a Number
- Converting Between %, Fraction and Decimal
- Word Problems on Comparing Quantities
- Word Problems on Profit and Loss
- Converting Percentage to Fraction
- Compound Interest (Half-Yearly & Quarterly)
