Introduction

In business, it's crucial to understand the dynamics between profit and loss, especially when dealing with similar pricing strategies. This article explores a scenario where two products are sold at the same price but result in different profit and loss percentages. By breaking down the cost prices and understanding the overall impact, we can derive an overall profit or loss percentage.

Scenario Overview

Consider two products with the same selling price:

First Product: A 25% profit margin. Second Product: A 14.28% loss.

Step-by-Step Solution

Define the Selling Price (SP)

Let the selling price of both products be SP.

Calculate the Cost Price (CP) of the First Product

Given that the profit percentage on the first product is 25, we can express this as:

SP CP_1 0.25 · CP_1 1.25 · CP_1

Rearranging gives:

CP_1 ( frac{SP}{1.25} 0.8 · SP )

Calculate the Cost Price (CP) of the Second Product

Given that the loss percentage on the second product is 14.28, this means:

SP CP_2 - 0.1428 · CP_2 0.8572 · CP_2

Rearranging gives:

CP_2 ( frac{SP}{0.8572} approx 1.1667 · SP )

Calculate the Total Cost Price (CP_total)

Adding the cost prices of both products:

CP_total CP_1 CP_2 0.8 · SP 1.1667 · SP 1.9667 · SP

Calculate the Overall Profit or Loss

The overall profit or loss can be calculated as:

Total Profit or Loss SP_total - CP_total SP - 1.9667 · SP 2 · SP - 1.9667 · SP 0.0333 · SP

This indicates a profit of approximately ( 0.0333 · SP ).

Calculate the Overall Profit Percentage

Using the formula for overall profit percentage:

Profit Percentage ( left( frac{Total Profit}{CP_{total}} right) times 100 left( frac{0.0333 · SP}{1.9667 · SP} right) times 100 approx 1.69 % )

Therefore, the overall profit percentage is approximately 1.69%.

Additional Insights

The key takeaway is that even when the selling price is the same, the difference in cost prices leads to different profit and loss percentages. Understanding this can help in making better financial decisions in business.

Notes:

A profit is indicated when the total profit is positive. A loss is indicated when the total profit is negative.

Example with Different Selling Price

Consider a situation where the selling prices are the same but the cost prices differ:

First Good: 20% profit margin. Second Good: 10% loss margin.

Let SP 1.20 and CP 1 for the first good. Then for the second good, we have:

(0.90 · CP SP 1.20 )

Therefore, CP 1.20 / 0.90 1.33 for the second good.

Total CP 1 1.33 2.33, and Total SP 1.20 1.20 2.40.

Profit (frac{2.40 - 2.33}{2.33} times 100 frac{0.07}{2.33} times 100 approx 3% )

This indicates a profit of 3%.

In conclusion, understanding the dynamics between cost prices and selling prices is crucial for making informed business decisions. The overall profit percentage in our initial scenario is approximately 1.69%, and the example with different selling prices highlights how the overall profit can be calculated even when the selling prices are the same.