Determine the Original Cost Price from a Given Loss and Selling Price

Understanding how to calculate the original cost price when you know the selling price and loss percentage is a fundamental skill in financial and business analysis. This guide will walk through the process step by step, providing detailed explanations and practical examples to help you apply this concept effectively.

What is Cost Price and Loss?

Before diving into the calculation, it's crucial to understand the terms used in this context:

Cost Price (CP): The price at which an item is purchased or produced. Loss: The difference between the cost price and the selling price when the selling price is lower than the cost price.

Calculating the Original Cost Price from Given Data

The formula to calculate the original cost price when you know the selling price and the loss percentage is:

Cost Price (CP) (Selling Price (SP) / (100 - Loss Percentage)) × 100

Example Problem:

Suppose a book is sold for $1200 at a loss of 10%. What is the original cost price of the book?

Step-by-Step Solution:

Identify the given values: Selling Price (SP) $1200, Loss Percentage 10% Apply the formula: Cost Price (CP) (SP / (100 - Loss Percentage)) × 100 Substitute the values: CP (1200 / (100 - 10)) × 100 Perform the calculations: 100 - 10 90 1200 / 90 13.3333 (rounded to four decimal places) 13.3333 × 100 1333.33 Final Answer: The original cost price of the book is $1333.33.

Understanding the Calculation Process

The formula takes into account the loss percentage, which affects the selling price. When an item is sold at a loss, the selling price is less than the cost price. The difference between these two values is the loss. By rearranging the formula to solve for the cost price, we can determine the original price at which the item was purchased or produced.

Practical Applications

Understanding how to calculate cost price is essential in various business scenarios, including:

Evaluating financial performance Setting pricing strategies Improving profit margins .ColumnHeader 4: Implementing effective inventory management strategies

Conclusion

Mastering the calculation of the original cost price from the selling price and loss percentage is a vital skill for anyone involved in financial analysis, business management, or sales. Whether you are a small business owner, advisor, or student, being able to calculate the cost price accurately can help you make informed decisions and improve your financial outcomes.

Additional Resources

To deepen your understanding of cost price calculation, loss, and profit, consider exploring the following resources:

Math Is Fun: Loss Investopedia: Cost Price AccountingTools: Cost Price