A dishonest vendor professes to sell fruits at .the cost price but he uses a weight of 800 grams in place of 1 kg weight. Find his percentage gain

Options

A. `22%`
B. `24%`
C. `25%`
D. `30%`

Answer

To find the percentage gain of the dishonest vendor who sells fruits using a weight of 800 grams instead of 1 kg, we can follow these steps:

### Step-by-Step Solution:

1. **Assume the Cost Price of 1 kg of Fruits**:
Let's assume the cost price (CP) of 1 kg of fruits is ₹100.

2. **Calculate the Cost Price of 800 grams**:
Since 1 kg = 1000 grams, the cost price of 1 gram of fruit is:
\[ \text{Cost Price of 1 gram} = \frac{100 \text{ rupees}}{1000 \text{ grams}} = 0.1 \text{ rupees/gram} \]
Therefore, the cost price of 800 grams is:
\[ \text{Cost Price of 800 grams} = 0.1 \text{ rupees/gram} \times 800 \text{ grams} = 80 \text{ rupees} \]

3. **Determine the Selling Price**:
The vendor sells 800 grams as if it were 1 kg. Therefore, the selling price (SP) for 800 grams is:
\[ \text{Selling Price} = 100 \text{ rupees} \]

4. **Calculate the Profit**:
Profit can be calculated as:
\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} = 100 \text{ rupees} - 80 \text{ rupees} = 20 \text{ rupees} \]

5. **Calculate the Profit Percentage**:
The profit percentage is given by the formula:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{Cost Price}}\right) \times 100 \]
Substituting the values we have:
\[ \text{Profit Percentage} = \left(\frac{20 \text{ rupees}}{80 \text{ rupees}}\right) \times 100 = 25\% \]

### Final Answer:
The percentage gain of the dishonest vendor is **25%**.

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