A dishonest dealer professes to sell his goods at cost price but he uses a weight of 900 gm in place of 1 kg.
Find his gain per cent.

Options

A. `(100)/(3)%`
B. `(100)/(9)%`
C. `(200)/(3)%`
D. `(200)/(9)%`

Answer

To solve the problem, we need to determine the gain percentage of the dishonest dealer who uses a weight of 900 grams instead of 1 kilogram (1000 grams) while claiming to sell at cost price.

### Step-by-Step Solution:

1. **Understand the Cost Price (CP)**:
- Let's assume the cost price of 1 kg of goods is ₹100.

2. **Actual Weight Sold**:
- The dealer sells only 900 grams instead of 1000 grams.

3. **Selling Price (SP)**:
- Since the dealer sells at cost price, the selling price for 900 grams is also ₹100 (the same as the cost price for 1 kg).

4. **Cost Price of 900 grams**:
- To find the cost price of 900 grams, we calculate it as follows:
\[ \text{Cost Price of 900 grams} = \left(\frac{900}{1000}\right) \times 100 = ₹90 \]

5. **Gain Calculation**:
- Now, we can find the gain by subtracting the cost price of 900 grams from the selling price:
\[ \text{Gain} = \text{Selling Price} - \text{Cost Price of 900 grams} = ₹100 - ₹90 = ₹10 \]

6. **Gain Percentage Calculation**:
- To find the gain percentage, we use the formula:
\[ \text{Gain Percentage} = \left(\frac{\text{Gain}}{\text{Cost Price of 900 grams}}\right) \times 100 \]
- Substituting the values:
\[ \text{Gain Percentage} = \left(\frac{10}{90}\right) \times 100 \approx 11.11\% \]

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

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