E-commerce
Unveiling Profit Analysis: Solving a Complex Profit and Loss Puzzle
Understanding Profit and Loss Analysis in a Complex Scenario
Business mathematics, particularly calculations involving profit and loss, are essential for any business. This article delves into a complex scenario, involving the sale of two articles and the subsequent calculation of profit percentages to achieve specific overall financial goals. We will explore a detailed mathematical problem solving process to find the profit percentage of the second article when a specified overall profit is anticipated.
Introduction to the Problem
A business owner sold two articles, each for 525,600. For one of the articles, he achieved a profit of 20%. Our goal is to determine the profit percentage of the second article that ensures an overall profit of 50% on the total sale.
Step-by-Step Calculation
1. Calculate the Total Selling Price (SP total)
Since each article was sold for 525,600 and there are two articles, the total selling price is:
SPtotal 2 x 525,600 1,051,200
2. Determine the Overall Cost Price (CP total) for 50% Profit
To achieve a 50% profit margin, the total cost price must be such that the profit is 50% of the total cost price. Thus:
SPtotal 1.5 x CPtotal
CPtotal SPtotal / 1.5 1,051,200 / 1.5 700,800
3. Calculate the Cost Price of the First Article
For the first article, the business owner made a 20% profit. This means the selling price is 120% of the cost price. The cost price can be calculated as:
SP1 1.2 x CP1
CP1 SP1 / 1.2 525,600 / 1.2 438,000
4. Determine the Cost Price of the Second Article
The total cost price for both articles is known. Subtracting the cost price of the first article from the total gives:
CP2 CPtotal - CP1 700,800 - 438,000 262,800
5. Calculate the Profit for the Second Article
The selling price of the second article is the same as the first, 525,600, and the cost price is 262,800. The profit can be calculated as:
Profit2 SP2 - CP2 525,600 - 262,800 262,800
6. Determine the Profit Percentage for the Second Article
The profit percentage is given by:
Profit Percentage2 (Profit2 / CP2) x 100 (262,800 / 262,800) x 100 100%
Therefore, the profit percentage of the second article is 100%.
Conclusion
The detailed mathematical analysis, step by step, demonstrates that the profit percentage of the second article, when both articles are sold at 525,600 each, is 100% to achieve an overall profit of 50% on the total sale. This approach can be applied to similar business scenarios requiring precise financial planning and analysis.