Understanding Correct Discount and Tax Calculations: An Analysis

Frequent misinterpretations occur in the calculation of discounts and taxes, with statements and calculations ranging from simple to complex. One such scenario is Dan's argument: claiming that subtracting a 20% discount from the price and then adding 12% for GST and PST taxes equates to subtracting 8% directly from the price. This article will break down the correct reasoning and calculations behind these operations.

Context and Background: The Core Calculation

Let's evaluate Dan's error step by step. While Dan simplifies the process, the key to understanding the correct calculation is in recognizing how discounts and taxes are applied relative to the original price and the discounted price. For instance, if the original price is Rs. 100, let's apply Dan's logic and determine the final price in both cases to find the truth.

Case Study: Original Price of Rs. 100

Dan's Method: Apply 20% discount: 100 - 20 (20% of 100) 80 Apply 12% GST: 80 12% of 80 80 9.6 89.60

Direct 8% Discount Method: Apply 8% discount: 100 - 8 (8% of 100) 92

As illustrated, the final prices are different (89.60 vs. 92). Dan's method results in a lower final price, indicating that he incorrectly applied the tax after the direct subtraction of the discount.

Step-by-Step Breakdown of Correct Calculations

To further elucidate, let's explore the correct method to calculate the final price after applying both a discount and tax.

Correct Calculation Steps

Step 1: Apply the Discount Discount: 100 - 20% 80 Price after discount: 80 Step 2: Apply the Taxes TAX Calculation: 12% of 80 9.60 Add to Price: 80 (discounted price) 9.60 (tax) 89.60

The final correct price is 89.60, highlighting the difference from the 8% discount which would result in 92. This discrepancy is due to the way taxes are applied to the discounted price versus applying a single, combined percentage directly.

Generalizing the Concept

Let's generalize Dan's claim with a more complex scenario. Suppose the list price of the item is Rs. U:

General Formulas

1. Discounted Price with Taxes (Correct Method): Apply 20% discount: U - 20% of U 0.8U Add 12% tax on discounted price: 0.8U 12% of 0.8U 0.8U 0.096U 0.896U

2. Direct 8% Discount (Incorrect Method): Apply 8% discount: U - 8% of U 0.92U

From the above, it is evident that 0.896U is not equal to 0.92U. Thus, the correct discount and tax combined process results in a different final price.

Conclusion: The Importance of Order of Operations

In summary, Dan's argument incorrectly assumes that the order of operations (applying discount before tax and then directly subtracting again) does not affect the final price. The correct method involves applying the discount first and then applying the tax on the discounted price. This difference is significant, especially in retail and financial settings where small discrepancies can accumulate to large sums over time.

Related Topics and Keywords

Discount Calculation: The process of reducing the price of goods or services to increase sales or clear inventory. Tax Addition: The process of adding a percentage of the price before or after the discount is applied. Price Analysis: The evaluation of the pricing strategy and its impact on sales and customer perception.