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

Options

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

Answer

To solve the problem of the shopkeeper who uses a 930 gm weight instead of a 1 kg weight while professing to sell at cost price, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Weights**:
- The actual weight he should sell is 1 kg, which is equal to 1000 grams.
- The weight he actually sells is 930 grams.

2. **Calculate the Difference in Weight**:
- The difference between the actual weight and the weight used by the shopkeeper is:
\[ 1000 \text{ grams} - 930 \text{ grams} = 70 \text{ grams} \]
- This means the shopkeeper is effectively saving 70 grams of goods.

3. **Determine the Cost Price (CP)**:
- Let's assume the cost price for 1 kg (1000 grams) of goods is \( CP \).
- Therefore, the cost price for 930 grams can be calculated as:
\[ CP_{930} = \frac{930}{1000} \times CP = 0.93 \times CP \]

4. **Selling Price (SP)**:
- The shopkeeper sells 930 grams at the price of 1 kg (1000 grams), which means:
\[ SP_{930} = CP \]

5. **Calculate Profit**:
- Profit can be calculated as:
\[ \text{Profit} = SP - CP_{930} = CP - (0.93 \times CP) = 0.07 \times CP \]

6. **Calculate Profit Percentage**:
- Profit percentage is calculated using the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{CP_{930}} \right) \times 100 \]
- Substituting the values:
\[ \text{Profit Percentage} = \left( \frac{0.07 \times CP}{0.93 \times CP} \right) \times 100 \]
- The \( CP \) cancels out:
\[ \text{Profit Percentage} = \left( \frac{0.07}{0.93} \right) \times 100 \]

7. **Perform the Calculation**:
- Now, calculate \( \frac{0.07}{0.93} \):
\[ \frac{0.07}{0.93} \approx 0.0753 \]
- Multiply by 100 to get the percentage:
\[ \text{Profit Percentage} \approx 7.53\% \]

### Final Answer:
The profit percentage of the shopkeeper is approximately **7.53%**.