Profit Calculation in Oranges Purchase and Selling

In business, understanding how to calculate profit and loss is a fundamental skill, especially when dealing with commodities like fruits. This article will explore a real-world example of a man who bought oranges for a certain price and sold them at a higher rate. The core of this example involves understanding the concepts of cost price (CP) and selling price (SP), and how they can be used to calculate profit, a critical aspect of financial management.

Case Analysis: A Man's Oranges Business

Let's analyze the transaction of this man. He buys oranges at the rate of Rs. 2 for 6, and sells the whole lot at the rate of Rs. 3 for 7. The total profit he earned from this transaction was Rs. 20.

Step-by-Step Calculation

Step 1: Determine the Cost Price (CP) and Selling Price (SP) per Orange

CP of 1 orange: 15 rupees for 3 oranges translates to Rs. 5 per orange (15/3 5).

SP of 1 orange: 24 rupees for 4 oranges means Rs. 6 per orange (24/4 6).

Step 2: Calculate the Profit Per Orange

The profit per orange is the difference between the SP and CP:

Profit SP - CP 6 - 5 1 Rupee per orange.

Step 3: Determine the Total Profit and Number of Oranges Sold

The total profit is Rs. 20. Therefore, the number of oranges sold is:

Total oranges 120/1 120 oranges.

Additional Scenarios

Purchase and Selling at Different Rates

He bought at the rate of 3 oranges for 15 rupees, CP 5 rupees per orange (15/3 5). He sold at the rate of 4 oranges for 24 rupees, SP 6 rupees per orange (24/4 6). Profit SP - CP 6 - 5 1Rupee per orange.

Equation-Based Approach

Assuming the total number of oranges bought is x, then:

CP: 2/6x x/3

SP: 3/7x 3x/7

Profit: 3x/7 - x/3 2x/21 20 (Given)

2x 420 rarr; X 210

Alternatives and Variations

Let's explore a few variations of this scenario to broaden our understanding:

Variation 1: Buying at Rs. 5 per Dozen

He buys x dozen at Rs. 5/dozen and sells the same amount at Rs. 4/dozen.

Total CP: 5x4x 9x Rs.

Total SP: 11/2×2x 11x Rs.

Profit: SP - CP 11x - 9x 2x Rs.

Ratio of Profit: 2x/50 2x/m; 1/50 1/m; m 50.

Therefore, he bought 50 dozens of oranges.

Variation 2: Buying at 4.50 per Dozen

He buys one dozen at Rs. 5 and sells at Rs. 5.50.

Total CP: 9 for two dozens 4.50 per dozen.

Total SP: 5.50 per dozen.

Profit per dozen: 5.50 - 4.50 1.00.

To earn a profit of Rs. 50, 50 dozen oranges are sold.

Variation 3: Selling at Re. 1 per 4 Oranges

He earned a total profit of Rs. 26, where the SP is Rs. 1 for 4 oranges.

No. of oranges sold must be 26 × 4 104.

Given the difference between the no. of oranges purchased and sold is 2:

104 ÷ 2 52.

He bought 52 × 6 312 oranges and sold 52 × 4 208.

Profit SP - CP Rs. 78 - Rs. 52 Rs. 26. Correct.

Conclusion

This case study illustrates the importance of understanding cost price and selling price in business transactions. By accurately calculating these figures, one can determine the profit or loss, and make informed decisions regarding pricing and quantity.