Calculating Discount Amount after VAT Application

Understanding how to calculate the discount amount in a scenario where VAT (Value Added Tax) is applied can sometimes be confusing. Let's break down the process with an example where a discount of 10% is allowed on the marked price of a television, followed by the addition of 15% VAT, resulting in a final price of Rs. 16720. The goal is to determine the amount given in the discount.

Introduction to VAT and Discount Calculations

Value Added Tax (VAT) is a type of consumption tax that is added to the price of a product at each stage of the supply chain. This tax amount is paid by the end consumer, and it is collected by the government at the point of sale. A discount is a reduction in the price of the product, typically expressed as a percentage of the marked price.

Step-by-Step Calculation

1. Let M denote the marked price of the given television.

2. After applying a 10% discount, the price becomes 90% of the marked price, which is represented mathematically as 0.9M.

3. Then, a 15% VAT is added to the discounted price. Therefore, the equation can be written as:

0.9M × 1.15 16720

4. Solving the equation:

M 16720 / (1.15 × 0.90) 16154.59

5. The discounted amount can be calculated as:

10% of M 0.10 × 16154.59 1615.46

Thus, the discount amount given is Rs. 1615.46.

Alternative Calculation Method

An alternative method to solve this problem involves breaking down the steps:

Let's assume M as the marked price. After a discount of 10%, the price becomes 0.9M. When 15% VAT is applied to this price, the final price is 0.9M × 1.15 16720.

Solving for M:

M 16720 / 1.035 16154.59

The discount amount: 0.10 × 16154.59 1615.46.

Verification of Calculation

To verify, we can cross-check the calculations:

Discounted Price 16154.59 - 1615.46 14539.13 VAT Applied 14539.13 × 15% 2180.87 Final Price 14539.13 2180.87 16720

This confirms that the final price is indeed Rs. 16720, validating the calculations.

Key Concepts

Marked Price (M): The advertised or original price of a product before any discounts or taxes. VAT: A consumption tax applied on the value added to a product at each stage of the supply chain. Discount Amount: The difference between the marked price and the selling price after applying a discount.

Understanding these concepts is crucial for managing finances and making informed decisions in retail environments.