Understanding Profit Calculation in Retail: A Case Study with Discount and Tax Considerations

Understanding how profit is calculated in retail scenarios is crucial for shopkeepers and businesses alike. This article delves into a specific scenario where a shopkeeper marked a tag price on an item, offered a discount, and included tax to determine the cost price, while making a 40% profit.

Problem Statement

A shopkeeper marks a tag price on an item in such a way that after allowing a 30% discount, a 40% profit is made. If the tag price of the item is Rs. 460, what is the cost price?

Methodology and Solution

Let the cost price (CP) of the article be Rs. X.

Step 1: Marked Price (MP)

Marked Price (MP) is 140% of the cost price. MP 1.4X

Step 2: Selling Price (SP) after discount

The selling price after a 30% discount is calculated as:

SP after discount MP - Discount SP after discount 1.4X - 224

Step 3: Selling Price (SP) after tax

The final selling price after including 10% tax is:

SP after tax SP after discount * 110% 1.1 * (1.4X - 224) SP after tax 1.54X - 246.4

Step 4: Profit Calculation

The profit is defined as the selling price after tax minus the cost price:

Profit SP after tax - CP 158.6 1.54X - 246.4 - X 158.6 0.54X - 246.4 0.54X 405 X 405 / 0.54 750

Hence, the cost price of the article is Rs. 750.

Verification

To verify the solution, let's check the calculations:

Marked Price (MP) 1.4 * 750 Rs. 1050 After discount (30% off): 1050 - 224 Rs. 826 After adding 10% tax: 826 * 1.1 Rs. 908.6 Profit 908.6 - 750 Rs. 158.6 The selling price after profit 908.6 - 158.6 Rs. 750 (which confirms the original cost price)

Conclusion

Through this detailed solution, it is evident that the shopkeeper achieved a 40% profit by marking the item at Rs. 750 and then applying a 30% discount followed by a 10% tax on the final selling price. This method guarantees a consistent profit margin in retail scenarios.

Keywords

Profit calculation, retail pricing, discount and tax impact