Calculating Gain Percentage: A Practical Example with Oranges

In the world of business, understanding the relationship between cost price, selling price, and gain percentage is crucial for profitable transactions. This article will guide you through a straightforward problem where the selling price of two oranges is the same as the cost price of three oranges. We will then walk you through the calculations to determine the gain percentage.

Problem Statement

The problem states that the selling price (SP) of two oranges is equal to the cost price (CP) of three oranges. Our goal is to find the gain percentage in this transaction.

Define Variables

C: Let the cost price of one orange be C. Cp3: Therefore, the cost price of three oranges is 3C. S: Let the selling price of one orange be S. Cp2: Therefore, the selling price of two oranges is 2S.

Set Up the Equation

According to the given information:

2S 3C

Find the Selling Price in Terms of Cost Price

Rearranging the equation gives:

S frac{3C}{2}

Calculate Profit

The profit for selling one orange can be calculated as:

Profit per orange S - C frac{3C}{2} - C frac{3C}{2} - frac{2C}{2} frac{C}{2}

Calculate Gain Percentage

The gain percentage is calculated as:

Gain Percentage left(frac{text{Profit}}{text{Cost Price}}right) times 100

Substituting the values:

Gain Percentage left(frac{frac{C}{2}}{C}right) times 100 left(frac{1}{2}right) times 100 50%

Closer Look at the Calculation

To further clarify, let's break down the process with an example:

Let the CP per orange be 4 units. Then, the CP of 3 oranges is 12 units.

The SP of 2 oranges equals 12 units, so the SP per orange is 6 units.

Gain SP - CP 6 - 4 2 units

Gain Percentage left(frac{2}{4}right) times 100 50%

Alternative Example

Let the CP of one orange be the variable 'x'. Thus, the CP of 3 oranges is 3x.

The SP of 2 oranges equals 3x, so the SP per orange is 1.5x.

CP of 2 oranges 2x

Profit on sales of 2 oranges 1.5x - 2x -0.5x (This is incorrect due to a flawed setup; the correct setup is as follows:)

Correct Setup: SP of 3 oranges 1.5x, and CP of 3 oranges 1.5x.

Gain 1.5x - 1.5x 0 (Correct, but the gain percentage is calculated differently:)

Gain Percentage left(frac{1.5x - 1.5x}{1.5x}right) times 100 50%

Conclusion

Through the above examples and calculations, it is evident that the gain percentage in this scenario is 50%. This calculation is a practical example that can be applied to similar problems in various business contexts.