Introduction

Profit and loss calculations are essential for any business owner, especially when it comes to understanding the true cost of goods sold. This article explains how to calculate the cost price of an item based on the marked price, discount, and the profit percentage. We'll delve into an example involving a TV sold at a 20% profit and see how changes in the cost and selling prices can affect the profit percentage.

Understanding the Basics

Before we dive into the problem, let's briefly review the essential formulas and concepts:

Profit: Profit is calculated as the selling price (SP) minus the cost price (CP): Sales - Cost Profit Selling Price: The selling price can be derived from the marked price (MP) and the discount: Selling price marked price - discount Profit Percentage: The profit percentage is calculated as: (Profit / CP) * 100

Given Problem and Solution

Let's consider the following problem:

Rakesh sells a TV at a 20% profit. If both the cost price (CP) and the selling price (SP) had been 1000 less, his profit would have been 25%. What was the actual cost price of the TV?

Example 1: Analyzing the Given Problem

Let's assume the cost price of the TV is x. Given that the TV is sold at a 20% profit, the selling price would be:

SP 800 - 20% of 800 640

To calculate the actual cost price, we use the formula:

640 - x x * 25%

Simplifying this, we get:

640 - x 0.25x

640 0.25x x 1.25x

x 640 / 1.25

x 512

Verification

To verify the solution, we can recalculate the profit percentage:

Profit SP - CP 640 - 512 128

Profit as a percentage of cost (128 / 512) * 100 25%

Alternative Calculation Methods

There are multiple ways to solve this problem, which include the following:

Method 1: Given marked price (MP) 800, discount 20%, selling price (SP) 800 - 20% of 800 640. The profit percentage is 25%, so we use the formula to calculate the cost price (CP): Method 2: Using the same marked price and discount, calculate the selling price and then determine the cost price based on the profit percentage. Method 3: Let the marked price (MP) 100, then the selling price after a 20% discount is 80. Using the relationship between CP and SP, we can find the actual cost price. Method 4: Let the cost price (CP) be Y. Given, SP 1.2Y and if CP Y - 1000, and SP 1.2Y - 1000. With a profit of 25%, we can solve for Y as follows:

Solving with Method 4

Let the cost price (CP) be Y. Given, the profit percentage is 25%, so:

SP 1.2Y

Given SP - 1000 1.25% of (CP - 1000), we can solve for Y:

1.2Y - 1000 1.25% of (Y - 1000)

1.2Y - 1000 0.0125(Y - 1000)

1.2Y - 1000 0.0125Y - 12.5

1.1875Y 1000 - 12.5

1.1875Y 987.5

Y 987.5 / 1.1875

Y 833.33 (approximately)

Conclusion

Understanding profit percentages, selling prices, and cost prices can help business owners make informed decisions. The given problem and its various solutions demonstrate how these formulas can be applied to real-world scenarios. By practicing such problems, one can develop better financial acumen and improve overall business performance.