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Mastering discount problems is essential for students aiming to excel in mathematics, especially in topics related to percentages and real-world applications. Practice is the key to understanding how discounts work and how to solve related problems efficiently. In this article, we will explore various discount problems with complete solutions to help students build confidence and improve their problem-solving skills.
Understanding Discount Problems
A discount is a reduction in the original price of an item, usually expressed as a percentage. When solving discount problems, the main goal is to find the discounted price or the original price, given specific information about the discount percentage and the final price.
Common Types of Discount Problems
- Finding the discounted price when the original price and discount percentage are known.
- Calculating the original price when the discounted price and discount percentage are given.
- Determining the discount percentage when the original and discounted prices are known.
Example 1: Finding the Discounted Price
Suppose an item costs ₹2000 and is offered at a 15% discount. What is the discounted price?
Solution:
Step 1: Find the amount of discount:
Discount = (Discount percentage / 100) × Original price
Discount = (15 / 100) × 2000 = 0.15 × 2000 = ₹300
Step 2: Subtract the discount from the original price:
Discounted price = Original price – Discount = ₹2000 – ₹300 = ₹1700
Answer: The discounted price is ₹1700.
Example 2: Calculating the Original Price
An item is sold at ₹850 after a 10% discount. What was the original price?
Solution:
Step 1: Let the original price be ₹x.
Since the discount is 10%, the selling price is 90% of the original price:
0.9 × x = ₹850
Step 2: Solve for x:
x = ₹850 / 0.9 ≈ ₹944.44
Answer: The original price was approximately ₹944.44.
Example 3: Finding the Discount Percentage
An item originally costs ₹1500 and is now available at ₹1200. What is the discount percentage?
Solution:
Step 1: Find the amount of discount:
Discount = Original price – Discounted price = ₹1500 – ₹1200 = ₹300
Step 2: Calculate the discount percentage:
Discount percentage = (Discount / Original price) × 100 = (₹300 / ₹1500) × 100 = 0.2 × 100 = 20%
Answer: The discount percentage is 20%.
Practice Problems
- Find the discounted price of an item costing ₹5000 with a 20% discount.
- An item is sold at ₹1800 after a 10% discount. What was the original price?
- The original price of an item is ₹2400. If the discount offered is 25%, what is the selling price?
- Calculate the discount percentage if an item originally costs ₹3200 and is now sold at ₹2560.
Practicing these problems regularly will help you become more confident in solving discount-related questions. Remember to carefully identify what is given and what you need to find, and apply the appropriate formulas accordingly.