Mastering Discount and Net Discount for Competitive Exams
Understanding discounts is crucial for excelling in the quantitative aptitude sections of competitive exams like the CAT. This module will demystify the concepts of single discount and net discount, equipping you with the skills to solve related problems efficiently.
Understanding Single Discount
A single discount is a straightforward reduction in price offered on an item. It's typically expressed as a percentage of the original marked price (MP).
Discount is a price reduction from the marked price.
The discount amount is calculated by multiplying the marked price by the discount percentage. The selling price (SP) is then the marked price minus the discount amount.
Formula for Single Discount: Discount Amount = Marked Price (MP) × (Discount Percentage / 100) Selling Price (SP) = Marked Price (MP) - Discount Amount Alternatively, SP = MP × (1 - Discount Percentage / 100)
Discount Amount = 500 × (20/100) = ₹100. Selling Price = 500 - 100 = ₹400.
Understanding Net Discount
When multiple discounts are offered sequentially on an item, we talk about successive discounts. The net discount is the single equivalent discount that would result in the same final selling price.
It's important to note that successive discounts are not simply added together. For example, a 10% discount followed by a 20% discount does not equal a 30% discount.
Net discount is the combined effect of successive discounts.
To find the net discount, we first calculate the selling price after each successive discount. The net discount is then the difference between the original marked price and the final selling price, expressed as a percentage of the marked price.
Let the marked price be MP. First Discount = D1% Price after first discount = MP × (1 - D1/100) Second Discount = D2% Final Selling Price = [MP × (1 - D1/100)] × (1 - D2/100) Net Discount Amount = MP - Final Selling Price Net Discount Percentage = (Net Discount Amount / MP) × 100 Alternatively, Net Discount Percentage = 100 - [100 × (1 - D1/100) × (1 - D2/100)]
A common shortcut for two successive discounts D1% and D2% is: Net Discount % = (D1 + D2 - (D1 × D2)/100)%. This formula directly gives the equivalent single discount.
Using the shortcut: Net Discount % = (10 + 20 - (10 × 20)/100)% = (30 - 2)% = 28%. Alternatively, Price after 10% discount = 1000 × (90/100) = 900. Price after 20% discount on 900 = 900 × (80/100) = 720. Net discount amount = 1000 - 720 = 280. Net discount % = (280/1000) × 100 = 28%.
Applying Concepts to Exam Problems
Exam questions often involve scenarios where you need to calculate the marked price given the selling price and discounts, or vice versa. Understanding the relationship between marked price, selling price, discount, and net discount is key to solving these efficiently. Practice with various question types to build speed and accuracy.
Visualizing the discount process helps solidify understanding. Imagine a price tag on an item. The Marked Price (MP) is the initial price shown. A discount is like peeling off a portion of that price. When multiple discounts are applied, it's like peeling off layers, and the net discount is the total amount peeled off compared to the original price.
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Learning Resources
This resource provides clear explanations and solved examples for discount calculations, including successive discounts.
A comprehensive guide covering various aspects of discounts, with formulas and practice problems relevant to competitive exams.
This blog post focuses specifically on CAT exam preparation, offering insights and strategies for discount-related questions.
Provides a concise summary of formulas and concepts related to profit, loss, and discount, useful for quick revision.
A video tutorial that visually explains the concept of successive discounts and how to calculate the net discount.
Offers a set of practice questions with solutions to help learners reinforce their understanding of discount concepts.
A video lesson focusing on Profit, Loss, and Discount for CAT aspirants, covering key strategies and problem-solving techniques.
Explains the fundamental definition of discount and its different types with illustrative examples.
Provides a general overview of profit and loss concepts, which are foundational to understanding discounts.
A blog post from a reputable CAT coaching institute, offering tips and strategies for mastering discount-related topics.