A vendor bought lemons at 6 for a rupee and sold them at 4 for a rupee. His gain% is

Options

A. 50%
B. 40%
C. `33 1/3%`
D. `16 2/3%`

Answer

To find the gain percentage of the vendor who bought lemons and sold them at different prices, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the Cost Price (CP) of 1 Lemon:**
The vendor bought 6 lemons for 1 rupee.
\[ \text{Cost Price of 1 lemon} = \frac{1 \text{ rupee}}{6} = \frac{1}{6} \text{ rupees} \]

2. **Determine the Selling Price (SP) of 1 Lemon:**
The vendor sold 4 lemons for 1 rupee.
\[ \text{Selling Price of 1 lemon} = \frac{1 \text{ rupee}}{4} = \frac{1}{4} \text{ rupees} \]

3. **Calculate the Gain:**
Gain is calculated as the Selling Price minus the Cost Price.
\[ \text{Gain} = \text{SP} - \text{CP} = \frac{1}{4} - \frac{1}{6} \]
To subtract these fractions, we need a common denominator. The least common multiple (LCM) of 4 and 6 is 12.
\[ \frac{1}{4} = \frac{3}{12} \quad \text{and} \quad \frac{1}{6} = \frac{2}{12} \]
Thus,
\[ \text{Gain} = \frac{3}{12} - \frac{2}{12} = \frac{1}{12} \text{ rupees} \]

4. **Calculate the Gain Percentage:**
Gain percentage is calculated using the formula:
\[ \text{Gain Percentage} = \left( \frac{\text{Gain}}{\text{CP}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Gain Percentage} = \left( \frac{\frac{1}{12}}{\frac{1}{6}} \right) \times 100 \]
Dividing the fractions:
\[ \frac{\frac{1}{12}}{\frac{1}{6}} = \frac{1}{12} \times \frac{6}{1} = \frac{6}{12} = \frac{1}{2} \]
Therefore,
\[ \text{Gain Percentage} = \frac{1}{2} \times 100 = 50\% \]

### Final Answer:
The gain percentage of the vendor is **50%**.