The Selling Price and Profit/Loss Percentage: A Comprehensive Analysis

When two items are sold at the same selling price, one at a profit and the other at a loss, the overall profit or loss can be confusing. This article delves into the calculations and explains how to accurately determine the effective profit or loss percentage in such scenarios.

Introduction

In business and economics, understanding the relationship between cost price, selling price, profit, and loss is crucial. This article focuses on a specific scenario where two articles are sold at the same selling price, with one article yielding a profit of 25% and the other resulting in a loss of 25%. We will provide a detailed analysis of how to calculate the effective profit or loss percentage and the overall loss or gain in such situations.

Calculation Methodology

Step-by-Step Calculation Example

Let's consider two articles sold at the same selling price ( S ). The first article is sold at a profit of 25%, while the second article is sold at a loss of 25%.

First Article

Let the cost price (CP) of the first article be ( CP_1 ). Given a profit of 25%, the selling price (SP) of the first article can be expressed as: [ S CP_1 times 1.25 Rightarrow CP_1 frac{S}{1.25} frac{4S}{5} ]

Second Article

Let the cost price of the second article be ( CP_2 ). Given a loss of 25%, the selling price (SP) of the second article can be expressed as: [ S CP_2 times 0.75 Rightarrow CP_2 frac{S}{0.75} frac{4S}{3} ]

Total Cost Price and Selling Price

Total cost price (CP) of both items: [ CP_1 CP_2 frac{4S}{5} frac{4S}{3} frac{12S}{15} frac{20S}{15} frac{32S}{15} ] Total selling price (SP) of both items: [ SP_1 SP_2 S S 2S ]

Effective Profit or Loss

The effective profit or loss can be calculated as: [ text{Effective Profit/Loss} text{Total SP} - text{Total CP} 2S - frac{32S}{15} frac{30S}{15} - frac{32S}{15} -frac{2S}{15} ]

This shows a loss of ( frac{2S}{15} ).

Effective Loss Percentage

The effective loss percentage is calculated as: [ text{Effective Loss Percentage} left( frac{frac{2S}{15}}{frac{32S}{15}} right) times 100 left( frac{2}{32} right) times 100 frac{1}{16} times 100 6.25% ]

The effective loss percentage in this case is 6.25%.

Practical Example with Given Selling Price

Let's assume the selling price of each item is $100.

First Good

The cost price (CP) of the first good is $90.91 and the profit is $10.

Second Good

The cost price (CP) of the second good is $111.11 and the loss is $10.

Total Cost Price and Selling Price

Total cost price: $202.02. Total selling price: $200.

Overall Loss Percentage

The overall loss percentage is calculated as:

[ text{Overall Loss Percentage} left( frac{202.02 - 200}{202.02} right) times 100 1% ]

Thus, the overall loss percentage is 1%.

Key Insights

From our calculations, we can understand the importance of correctly assessing cost prices and the impact of different profit and loss percentages on the overall financial outcome.

Conclusion

This article provides a detailed breakdown of how to calculate the effective profit or loss percentage when selling items at the same price. Understanding such calculations can help businesses make informed decisions regarding pricing and inventory management.