Calculating Profit Percentage in Orange Sales

When dealing with sales and purchases, it is essential to understand the profit percentage for various transactions. Here, we will explore a specific scenario involving the purchase and sale of oranges, a common real-world example used to illustrate the concept of profit percentage.

Scenario Overview

A trader buys 18 oranges for a rupee and sells them at a rate of 12 oranges for a rupee. This article delves into the process to determine the profit percentage in this transaction. It also includes alternative methods to solve similar problems involving oranges, showing the importance of understanding cost price (CP) and selling price (SP).

Understanding the Cost Price (CP) and Selling Price (SP)

To calculate the profit percentage, we begin by identifying the cost price (CP) and selling price (SP) of the oranges.

Cost Price (CP) for One Orange

The trader buys 18 oranges for 1 rupee. Therefore, the cost price (CP) per orange is:

CP per orange frac{1 text{ rupee}}{18} frac{1}{18} text{ rupee}

Selling Price (SP) for One Orange

The trader sells 12 oranges for 1 rupee. Therefore, the selling price (SP) per orange is:

SP per orange frac{1 text{ rupee}}{12} frac{1}{12} text{ rupee}

Calculating the Profit per Orange

Profit per orange can now be calculated as follows:

Profit SP - CP frac{1}{12} - frac{1}{18}

To subtract these fractions, we need a common denominator, which is 36:

frac{1}{12} frac{3}{36} text{ and } frac{1}{18} frac{2}{36}

Hence, the profit per orange is:

Profit frac{3}{36} - frac{2}{36} frac{1}{36} text{ rupee}

Calculating the Profit Percentage

The formula to calculate the profit percentage is given by:

Profit Percentage left(frac{text{Profit}}{text{CP}} times 100right)%

Substituting the values, we get:

Profit Percentage left(frac{frac{1}{36}}{frac{1}{18}} times 100right)%

By simplifying the fraction:

frac{frac{1}{36}}{frac{1}{18}} frac{1}{36} times frac{18}{1} frac{18}{36} frac{1}{2}

Hence, the profit percentage is:

Profit Percentage frac{1}{2} times 100 50%end{code}

Alternative Methods to Solve the Problem

There are alternative methods to solve similar problems involving oranges. Here are a couple of techniques:

Method 1 - Equal Number of Oranges Purchased and Sold

If we aim to equalize the number of oranges bought and sold, the least common multiple (LCM) of 18 and 12 is 36.

CP (Cost Price) of 36 oranges frac{36}{18} 2 rupees

SP (Selling Price) of 36 oranges frac{36}{12} 3 rupees

Hence, profit 3 - 2 1 rupee

Profit percentage frac{1}{2} times 100 50%end{p}

Method 2 - Analytical Approach

The trader recovers the cost of 18 oranges by selling 12 oranges. The remaining 6 oranges reflect profit.

Profit frac{6}{12} times 100 50%end{p>

Conclusion

By understanding and applying the concepts of CP and SP, the profit percentage can be accurately calculated in real-world scenarios like the one involving oranges. This example showcases the versatile methods available to determine profit percentages, which are invaluable in business and financial analysis.