Let's break the solution down step-by-step to determine the gain percentage:
1. Understanding the terms:
- Cost price per dozen (12 oranges) = ₹ 26
- Selling price for 5 oranges = ₹ 13
2. Calculating the cost price per orange:
Since there are 12 oranges in a dozen, the cost price per orange is calculated by dividing the total cost by 12.
[tex]\[
\text{Cost price per orange} = \frac{₹ 26}{12} = ₹ 2.1666666666666665
\][/tex]
3. Calculating the selling price per orange:
Since the selling price for 5 oranges is ₹ 13, the selling price per orange is calculated by dividing the total selling price by 5.
[tex]\[
\text{Selling price per orange} = \frac{₹ 13}{5} = ₹ 2.6
\][/tex]
4. Determining the profit per orange:
The profit made on each orange is the difference between the selling price per orange and the cost price per orange.
[tex]\[
\text{Profit per orange} = \text{Selling price per orange} - \text{Cost price per orange} = ₹ 2.6 - ₹ 2.1666666666666665 = ₹ 0.43333333333333357
\][/tex]
5. Calculating the profit percentage:
The profit percentage is calculated by dividing the profit per orange by the cost price per orange and then multiplying by 100.
[tex]\[
\text{Profit percentage} = \left(\frac{\text{Profit per orange}}{\text{Cost price per orange}}\right) \times 100 = \left(\frac{₹ 0.43333333333333357}{₹ 2.1666666666666665}\right) \times 100 = 20.00000000000001\%
\][/tex]
Thus, the vendor's gain percentage is approximately [tex]\( 20\% \)[/tex].
