A vendor buys oranges at Rs 26 per dozen and sells them at 5 for Rs 13. Find his gain percent.

Options

A. `20%`
B. `30%`
C. `40%`
D. `50%`

Explanation

To find the gain percent of the vendor who buys oranges at Rs 26 per dozen and sells them at 5 for Rs 13, we can follow these steps:

### Step 1: Calculate the Cost Price (CP) per orange
The vendor buys oranges at Rs 26 per dozen. Since there are 12 oranges in a dozen, we can calculate the cost price per orange.

\[ \text{Cost Price per orange} = \frac{\text{Cost Price per dozen}}{12} = \frac{26}{12} \approx 2.17 \text{ Rs} \]

### Step 2: Calculate the Selling Price (SP) per orange
The vendor sells 5 oranges for Rs 13. To find the selling price per orange, we divide the total selling price by the number of oranges sold.

\[ \text{Selling Price per orange} = \frac{\text{Selling Price for 5 oranges}}{5} = \frac{13}{5} = 2.6 \text{ Rs} \]

### Step 3: Calculate the Gain per orange
Now, we can find the gain by subtracting the cost price from the selling price.

\[ \text{Gain} = \text{Selling Price} - \text{Cost Price} = 2.6 - 2.17 = 0.43 \text{ Rs} \]

### Step 4: Calculate the Gain Percent
To find the gain percent, we use the formula:

\[ \text{Gain Percent} = \left(\frac{\text{Gain}}{\text{Cost Price}} \times 100\right) = \left(\frac{0.43}{2.17} \times 100\right) \approx 19.81\% \]

### Final Answer
The gain percent of the vendor is approximately **19.81%**.

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