Profit and Loss Calculations for Items Sold at Different Prices

Understanding profit and loss calculations is essential for businesses and consumers alike. This article explains how to calculate the cost price from the selling price and profit percentage, and then determine the profit or loss when the item is sold at a different price. We will use the example of an item sold for Rs. 180 with a profit of 10%, and then sold for Rs. 160 to calculate the new loss percentage.

Step 1: Calculate the Cost Price (CP)

When an item is sold for Rs. 180 with a profit of 10%, the selling price (SP) can be expressed as:

[text{SP} text{CP} 10% text{ of } text{CP} text{CP} 0.1 times text{CP} 1.1 times text{CP}]

Given that SP Rs. 180, we can solve for CP:

[text{CP} frac{180}{1.1} frac{1800}{11} approx 163.64]

Step 2: Calculate the New Selling Price (SP)

Now, if the item is sold for Rs. 160, we need to calculate the profit or loss:

[text{SP} 160]

Step 3: Calculate the Profit or Loss

To find the profit or loss, we compare the selling price with the cost price:

[text{Loss} text{CP} - text{SP} 163.64 - 160 3.64]

Step 4: Calculate the Percentage of Loss

The percentage of loss can be calculated using the formula:

[text{Percentage of Loss} left(frac{text{Loss}}{text{CP}}right) times 100]

[text{Percentage of Loss} left(frac{3.64}{163.64}right) times 100 approx 2.22%]

Therefore, if the item was sold for Rs. 160, there would have been a loss of approximately 2.22%.

Additional Example:

Consider another example where a book is sold for Rs. 27.50 with a 10% profit:

[text{Cost Price (CP)} frac{27.50}{110} times 100 25] [text{New Selling Price (SP)} 25.75] [text{Profit} 25.75 - 25 0.75] [text{Percentage of Profit} frac{0.75}{25} times 100 3%]

Conclusion

By using these steps, you can accurately calculate profit or loss percentages when the selling price changes. This knowledge is crucial for making informed decisions in business and managing financial resources effectively.