A trader has a weighing balance that shows 1,200 gm for a kilogram. He further marks up his cost price by 10%. Then the net profit percentage is

Options

A. `32%`
B. `23%`
C. `31.75%`
D. `23.50%`

Answer

To solve the problem step by step, we will analyze the situation of the trader and calculate the net profit percentage.

### Step 1: Understand the weight discrepancy
The trader uses a weighing balance that shows 1200 grams as 1 kilogram. This means when he sells what he claims is 1 kg, he is actually selling only 1200 grams.

### Step 2: Calculate the effective selling price
Let’s assume the cost price (CP) of 1 kg (1000 grams) is ₹100. Since he is selling 1200 grams as 1 kg, we need to determine the selling price (SP) for 1200 grams.

1. **Cost Price for 1200 grams**:
- If 1000 grams costs ₹100, then:
\[ \text{CP for 1200 grams} = \left(\frac{1200}{1000}\right) \times 100 = ₹120 \]

2. **Marking up the cost price by 10%**:
- The trader marks up his cost price by 10%. Therefore, the selling price (SP) will be:
\[ \text{SP} = \text{CP} + 10\% \text{ of CP} = 120 + 0.10 \times 120 = 120 + 12 = ₹132 \]

### Step 3: Calculate the profit
Now, we can calculate the profit made by the trader when he sells 1200 grams for ₹132.

1. **Profit Calculation**:
- Profit = Selling Price - Cost Price
\[ \text{Profit} = 132 - 120 = ₹12 \]

### Step 4: Calculate the profit percentage
To find the net profit percentage, we use the formula:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{Cost Price}}\right) \times 100 \]
Substituting the values:
\[ \text{Profit Percentage} = \left(\frac{12}{120}\right) \times 100 = 10\% \]

### Step 5: Adjust for the weight discrepancy
Since the trader is actually selling 1200 grams instead of 1000 grams, we need to account for this additional profit percentage:

1. **Effective Profit Percentage from Weight**:
- The profit from selling 1200 grams instead of 1000 grams is:
\[ \text{Effective Profit Percentage} = \left(\frac{200}{1000}\right) \times 100 = 20\% \]

### Step 6: Combine both profit percentages
Now, we combine the profit from the markup and the profit from the weight discrepancy:
\[ \text{Net Profit Percentage} = \text{Profit from markup} + \text{Profit from weight} \]
Using the formula:
\[ \text{Net Profit Percentage} = 20\% + 10\% + \left(\frac{20 \times 10}{100}\right) = 20 + 10 + 2 = 32\% \]

### Final Answer
The net profit percentage is **32%**.