A shopkeeper professes to sell his goods at cost price but uses a 930 gm weight instead of 1 kilogram weight. What will be the profit percentage of the shopkeeper?

Options

A. `3.76`
B. `7.52`
C. `9.85`
D. `10.36`

Answer

To determine the profit percentage of the shopkeeper who uses a 930 gm weight instead of a 1 kg weight while claiming to sell at cost price, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the weights involved**:
- The standard weight for 1 kg is 1000 grams.
- The shopkeeper uses a weight of 930 grams.

2. **Calculate the weight difference**:
- The difference in weight is \(1000 \text{ grams} - 930 \text{ grams} = 70 \text{ grams}\).
- This means the shopkeeper is shortchanging the customer by 70 grams.

3. **Determine the cost price (CP)**:
- Let's assume the cost price for 1 kg (1000 grams) is \(CP\).

4. **Selling price (SP)**:
- The shopkeeper sells 930 grams at the cost price of 1 kg, which is \(CP\).

5. **Calculate the effective cost price for 930 grams**:
- The cost price for 930 grams can be calculated as:
\[ \text{CP for 930 grams} = \frac{930}{1000} \times CP = 0.93 \times CP \]

6. **Calculate the profit**:
- The profit made by the shopkeeper when selling 930 grams is:
\[ \text{Profit} = \text{Selling Price} - \text{Cost Price for 930 grams} = CP - 0.93 \times CP = 0.07 \times CP \]

7. **Calculate the profit percentage**:
- The profit percentage can be calculated using the formula:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{Cost Price for 930 grams}}\right) \times 100 \]
- Substituting the values:
\[ \text{Profit Percentage} = \left(\frac{0.07 \times CP}{0.93 \times CP}\right) \times 100 \]
- The \(CP\) cancels out:
\[ \text{Profit Percentage} = \left(\frac{0.07}{0.93}\right) \times 100 \]

8. **Calculating the final value**:
- Performing the division:
\[ \frac{0.07}{0.93} \approx 0.07527 \]
- Now multiply by 100 to get the percentage:
\[ 0.07527 \times 100 \approx 7.527 \approx 7.52\% \]

### Conclusion:
The profit percentage of the shopkeeper is approximately **7.52%**.