A dealer professing to sell at cost price uses a 900 gms weight for a kilogram. His gain per cent is -

Options

A. 9
B. 10
C. 11
D. `(11)1/9`

Answer

To find the gain percentage of the dealer who uses a 900 g weight instead of a 1000 g weight while professing to sell at cost price, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Situation**: The dealer claims to sell 1 kg (1000 g) of a product at cost price but actually sells only 900 g.

2. **Calculate the Difference in Weight**:
\[ \text{Difference in weight} = 1000 \text{ g} - 900 \text{ g} = 100 \text{ g} \]

3. **Determine the Cost Price (CP)**:
Let's assume the cost price of 1 kg (1000 g) is \( CP \). Therefore, the cost price of 900 g can be calculated as:
\[ \text{CP of 900 g} = \frac{900}{1000} \times CP = 0.9 \times CP \]

4. **Selling Price (SP)**: The dealer sells 900 g at the cost price of 1 kg, which is \( CP \).

5. **Calculate the Gain**:
The gain made by the dealer when selling 900 g is:
\[ \text{Gain} = \text{Selling Price} - \text{Cost Price of 900 g} \]
\[ \text{Gain} = CP - (0.9 \times CP) = CP - 0.9 \times CP = 0.1 \times CP \]

6. **Calculate Gain Percentage**:
Gain percentage is calculated using the formula:
\[ \text{Gain Percentage} = \left( \frac{\text{Gain}}{\text{Cost Price of 900 g}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Gain Percentage} = \left( \frac{0.1 \times CP}{0.9 \times CP} \right) \times 100 \]
\[ \text{Gain Percentage} = \left( \frac{0.1}{0.9} \right) \times 100 \approx 11.11\% \]

### Final Answer:
The gain percentage of the dealer is approximately **11.11%**.

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