Calculating Percentage Gain or Loss: A Bicycle Sales Case Study

In the world of trading and sales, understanding the relationship between cost price, selling price, and profit or loss is crucial. This article will detail how a trader's situation can be analyzed through a real-life example involving a bicycle sold for 54,000 naira with a loss, and then re-evaluated to determine the gain or loss if sold for 57,600 naira.

Introduction to the Problem

Assume a trader sells a bicycle for 54,000 naira and incurs a loss of 10%. To find the cost price (CP) of the bicycle, we use the formula for loss:

Selling Price (SP) CP - (Loss Percentage * CP)

Step 1: Finding the Cost Price (CP)

The given selling price (SP) is 54,000 naira, and the loss percentage is 10%. Plugging these values into the formula, we get:

54,000 CP - (0.10 * CP)

This can be simplified to:

54,000 0.90 * CP

To solve for CP, we divide both sides by 0.90:

CP 54,000 / 0.90 60,000 naira

Step 2: Recalculating Gain or Loss for a New Selling Price

Now, let’s determine the gain or loss if the bicycle is sold for 57,600 naira. The new selling price (SP) is 57,600 naira. Using the cost price (CP) we calculated, we find the difference:

SP - CP 57,600 - 60,000 -2,400 naira

This difference represents a loss of 2,400 naira.

Step 3: Calculating the Percentage Loss

The percentage loss is calculated using the formula:

Percentage Loss (Loss / CP) * 100

Substituting the values:

Percentage Loss (2,400 / 60,000) * 100 4%

Conclusion

If the trader had sold the bicycle for 57,600 naira instead of 54,000 naira, he would have incurred a loss of 4%. This analysis can be applied to various trading and sales scenarios to make informed decisions.

Additional Insights and Tips

Understanding Cost Price and Selling Price: The cost price (CP) is the price at which an item is purchased, while the selling price (SP) is the price at which an item is sold.

Profit and Loss Formulas: Profit SP - CP and Loss CP - SP.

Percentage Calculations: To find the percentage profit or loss, divide the profit or loss by the cost price and multiply by 100.

By understanding these basic formulas and principles, traders can better manage their investments and sales, leading to improved financial performance.

Conclusion Summary

In summary, this example demonstrates how to calculate the cost price of an item based on a given selling price and loss percentage. It also illustrates how to recalculate the gain or loss and determine the percentage loss if the selling price changes. This knowledge is invaluable for any trader or sales professional aiming to optimize their business.

Key Takeaways

Use the formula for loss to find the cost price of an item. Recalculate the gain or loss based on a new selling price. Calculate the percentage loss to understand the financial impact.

By following these steps, traders can make more informed decisions and improve their profitability in the marketplace.