Understanding Discounts and Taxes: A Comprehensive Guide
When dealing with sales and purchases, understanding the relationship between marked price, discounts, and taxes is crucial. This article delves into the detailed calculations and provides a clearer understanding of these concepts through a specific example.
Selling Price Calculation with Discount and VAT
Scenario: An article is marked at Rs. 4500. After offering a certain discount and levying a 10% VAT, the final selling price becomes Rs. 4400. This article aims to find the discount percentage.
Step-by-Step Breakdown
Define Variables: Let the discount percentage be x. Calculate the Selling Price After Discount:[text{Selling Price after Discount} 4500 - frac{x}{100} times 4500 4500 left(1 - frac{x}{100}right)]
Add 10% VAT to the Selling Price:[text{Total Selling Price} left(4500 left(1 - frac{x}{100}right)right) times 1.10]
Solving the Equation
Set Up the Equation:[4500 times 1.10 left(1 - frac{x}{100}right) 4400]
Subtract 10% VAT:[4950 left(1 - frac{x}{100}right) 4400]
Divide Both Sides by 4950:[1 - frac{x}{100} frac{4400}{4950}]
Calculate the Ratio:[frac{4400}{4950} approx 0.8909quadtext{or}quad frac{44}{49}]
Rearrange the Equation:[1 - frac{x}{100} frac{44}{49}]
Solve for x:[frac{x}{100} 1 - frac{44}{49} frac{5}{49}] [x frac{5}{49} times 100 approx 10.2041]
Therefore, the discount percentage is approximately 10.20.
Additional Insight: Calculating Discount Amount
Alternatively, we can calculate the discount amount by finding the original price of the article before any discounts and taxes were applied. Given that the final price is Rs. 4400 and 10% VAT is added, the marked price before discount can be calculated as:
Steps: Determine the amount of tax on the marked price. Calculate the original price before the discount. Subtract the final price from the original price to find the discount amount.
Calculate the Total Amount of Tax:[text{Total Selling Price} div 1.10 4400 div 1.10 4000]
Find the Original Price Before Discount:[text{Original Price} 4000 div 0.90 4444.44]
Calculate the Discount Amount:[text{Discount Amount} 4500 - 4444.44 55.56]
However, using the initial method, the discount amount is approximately Rs. 298.30.
Conclusion and Further Reading
Understanding the relationship between marked prices, discounts, and taxes helps in making accurate assessments in sales and purchasing scenarios. This article provides a practical guide on how to calculate discount percentages and the actual discount amount using detailed step-by-step methods.
Key Learnings: Discount percentage calculation using the final selling price and original marked price. Calculating discount amount using the initial marked price and final selling price.