To solve this problem, we need to find the cost price per orange and the selling price per orange, then calculate the gain or loss percent.
### Step-by-Step Solution:
1. Find the Cost Price per Orange:
The vendor bought oranges at Rs. 20 for Rs. 56. To find the cost price per orange:
[tex]\[
\text{Cost Price per Orange} = \frac{20 \, \text{Rs}}{56 \, \text{oranges}}
\][/tex]
2. Find the Selling Price per Orange:
The vendor sold the oranges at Rs. 35 per dozen (12 oranges). To find the selling price per orange:
[tex]\[
\text{Selling Price per Orange} = \frac{35 \, \text{Rs}}{12 \, \text{oranges}}
\][/tex]
3. Calculate the Gain per Orange:
The gain per orange is the difference between the selling price per orange and the cost price per orange:
[tex]\[
\text{Gain per Orange} = \text{Selling Price per Orange} - \text{Cost Price per Orange}
\][/tex]
4. Calculate the Gain Percent:
The gain percent is calculated based on the cost price per orange. The formula for gain percent is:
[tex]\[
\text{Gain Percent} = \left( \frac{\text{Gain per Orange}}{\text{Cost Price per Orange}} \right) \times 100
\][/tex]
From our calculations, we have:
- Cost Price per Orange: [tex]\(\frac{20}{56} \approx 0.357143 \, \text{Rs}\)[/tex]
- Selling Price per Orange: [tex]\(\frac{35}{12} \approx 2.916667 \, \text{Rs}\)[/tex]
- Gain per Orange: [tex]\(2.916667 - 0.357143 \approx 2.559524 \, \text{Rs}\)[/tex]
- Gain Percent: [tex]\(\left( \frac{2.559524}{0.357143} \right) \times 100 \approx 716.67\% \)[/tex]
Thus, the vendor makes a gain, and the gain percent is approximately [tex]\(716.67\%\)[/tex].
None of the options given match the calculated gain percent. Therefore, we can conclude that the correct gain percent is not listed among the provided options, and the calculation yields a gain percent of approximately 716.67%.
