Calculate Cost Price With A 4% Loss On $105,000 Sale
#h1 Title: John sold an article for $105,000.00 at a loss of 4%. Find the cost price of the article.
In this article, we will delve into the problem of calculating the cost price of an article when it is sold at a loss. John sold an article for $105,000.00, incurring a loss of 4%. Our goal is to determine the original cost price of the article. This is a common type of problem in business mathematics and understanding how to solve it is crucial for anyone dealing with sales, pricing, and financial analysis. Let's break down the problem step by step to arrive at the correct solution.
Understanding the Problem
Before we dive into the calculations, let's clarify the key terms and concepts involved in this problem. The cost price is the original price at which John purchased the article. The selling price is the price at which John sold the article, which in this case is $105,000.00. The loss is the amount of money John lost in the transaction, expressed as a percentage of the cost price, which is 4%. To find the cost price, we need to reverse the calculation process that led to the loss. Understanding these concepts is crucial because it forms the basis for solving not only this problem but also a myriad of similar financial calculations. We will use the percentage loss formula to determine the original price, ensuring that we account for the reduction in value due to the loss.
The relationship between cost price, selling price, and loss can be expressed through a simple formula. When an item is sold at a loss, the selling price is less than the cost price. The loss amount is the difference between the cost price and the selling price. The percentage loss is calculated as the loss amount divided by the cost price, multiplied by 100. Mathematically, this is represented as:
Loss % = [(Cost Price - Selling Price) / Cost Price] * 100
In our case, we know the selling price and the loss percentage, and we need to find the cost price. Rearranging this formula to solve for the cost price will be our primary strategy. By understanding the interplay between these elements, we can effectively solve the problem and gain insight into how businesses manage pricing and profitability. This understanding extends beyond mere calculation; it helps in making informed decisions about buying and selling goods, ensuring that transactions are financially sound.
Setting up the Equation
To solve this problem, we need to translate the given information into a mathematical equation. We know that John sold the article at a loss of 4%. This means that the selling price ($105,000.00) represents 100% minus the loss percentage (4%) of the cost price. Let's denote the cost price as 'C'. Therefore, the selling price is 96% of the cost price. We can express this relationship as:
0. 96 * C = $105,000.00
This equation is the foundation for finding the cost price. It captures the essence of the problem by directly relating the selling price to the cost price, considering the loss incurred. Setting up the equation correctly is paramount because it dictates the accuracy of the final result. Each component of the equation represents a key aspect of the transaction. The coefficient 0.96 represents the remaining percentage of the cost price after accounting for the 4% loss, and the dollar amount represents the selling price received after the loss. The unknown variable, C, stands for the cost price, which we aim to determine. Once the equation is correctly set up, we can proceed with algebraic manipulation to isolate the variable and find its value. This step is critical in solving any word problem that involves percentage loss or gain.
Solving for the Cost Price
Now that we have our equation, 0.96 * C = $105,000.00, we can solve for the cost price (C). To isolate C, we need to divide both sides of the equation by 0.96. This is a fundamental algebraic operation that maintains the equality of the equation while allowing us to find the value of the unknown variable. Performing this division, we get:
C = $105,000.00 / 0.96
Carrying out this calculation will give us the cost price of the article. Division is the inverse operation of multiplication, and in this context, it helps us to undo the effect of the 4% loss on the original cost price. When we divide the selling price by 0.96, we are essentially scaling up the selling price to what it would have been without the loss. This step is crucial in financial calculations where we need to find the original value before a discount or loss. The result of this division will be the cost price, which is the amount John initially paid for the article. Solving for C in this equation is a straightforward process, but it requires a clear understanding of algebraic principles and the relationship between multiplication and division.
When you perform the division, you'll find:
C = $109,375.00
This means the original cost price of the article was $109,375.00. This result is vital as it indicates the amount John initially invested in the article before selling it at a loss. The calculated cost price helps in understanding the financial implications of the sale and the magnitude of the loss incurred. In a business context, knowing the cost price is essential for calculating profit margins, setting appropriate selling prices, and making informed decisions about inventory management. The cost price serves as a benchmark for evaluating the success of a transaction and the overall profitability of a business operation. Moreover, understanding how to calculate the cost price in situations involving losses is a fundamental skill in financial analysis, enabling stakeholders to assess the impact of market conditions and pricing strategies on business performance.
Verifying the Solution
To ensure the accuracy of our calculation, it's good practice to verify the solution. We found that the cost price of the article is $109,375.00. Now, let's calculate the 4% loss on this cost price and subtract it from the cost price to see if it matches the selling price of $105,000.00. First, we find the loss amount:
Loss Amount = 4% of $109,375.00
Loss Amount = 0.04 * $109,375.00
Loss Amount = $4,375.00
Next, we subtract this loss amount from the cost price:
Selling Price = Cost Price - Loss Amount
Selling Price = $109,375.00 - $4,375.00
Selling Price = $105,000.00
This matches the given selling price, confirming that our calculated cost price of $109,375.00 is correct. Verifying the solution is an important step in problem-solving as it helps to catch any errors in the calculations and ensures that the final answer is accurate. In this case, the verification process validates the method used to calculate the cost price and reinforces our confidence in the result. This practice is particularly crucial in financial calculations where accuracy is paramount, as even small errors can have significant implications. By verifying the solution, we not only ensure the correctness of the answer but also deepen our understanding of the underlying concepts and the relationships between the variables involved.
Conclusion
In conclusion, the cost price of the article that John sold for $105,000.00 at a 4% loss is $109,375.00. We arrived at this answer by setting up an equation that related the selling price to the cost price, considering the loss percentage. The steps involved understanding the relationship between cost price, selling price, and loss, translating the problem into a mathematical equation, solving for the cost price, and verifying the solution. This problem illustrates the practical application of percentage calculations in real-world business scenarios. Understanding how to calculate cost price, selling price, and profit or loss percentages is essential for anyone involved in buying, selling, or managing finances.
#h2 Key Takeaways
- Cost Price Calculation: To find the cost price when there is a loss, the formula
Cost Price = Selling Price / (1 - Loss Percentage)can be used. - Percentage Loss: The loss percentage is calculated as
(Loss Amount / Cost Price) * 100. - Verification: Always verify your solution by ensuring that the calculated cost price, when subjected to the given loss percentage, results in the selling price.
#h2 Practical Applications
The concepts discussed in this article have broad applications in various fields:
- Retail: Retailers use these calculations to determine the original price of goods, set selling prices, and calculate profit margins.
- Finance: Financial analysts use these concepts to assess the financial performance of businesses and investments.
- Real Estate: Real estate professionals apply these calculations to determine property values, assess investment returns, and negotiate sales prices.
- Personal Finance: Individuals can use these principles to make informed purchasing decisions, understand the impact of discounts and markdowns, and manage their personal finances effectively.
Understanding and applying these concepts is not only beneficial in academic settings but also crucial for making sound financial decisions in everyday life.
#h2 Final Answer
The correct answer is D. $N 109,375.00.
