A dishonest dealer professes to sell his goods at 10% loss. But he uses a false weight of 800 gm instead of kilogram weight. Thus his profit percentage is

Options

A. 0.12
B. 11`1/2`%
C. 8`1/2`%
D. 12`1/2`%

Answer

To solve the problem step by step, we will calculate the profit percentage of the dishonest dealer who sells goods at a 10% loss while using a false weight of 800 grams instead of 1 kilogram (1000 grams).

### Step-by-Step Solution:

1. **Assume the Cost Price (CP) for 1000 grams**:
Let's assume the cost price of 1000 grams of goods is ₹1000.

**Hint**: Start by defining a base value for the cost price to simplify calculations.

2. **Calculate the Selling Price (SP) at 10% Loss**:
Since the dealer sells at a 10% loss, the selling price can be calculated as:
\[ SP = CP - (10\% \text{ of } CP) = 1000 - (0.10 \times 1000) = 1000 - 100 = ₹900 \]

**Hint**: Remember that selling at a loss means you subtract the loss percentage from the cost price.

3. **Determine the Cost Price of 800 grams**:
The cost price for 800 grams can be calculated as follows:
\[ CP \text{ of } 800 \text{ grams} = \left(\frac{800}{1000}\right) \times 1000 = ₹800 \]

**Hint**: To find the cost price for a different weight, use a proportion based on the total weight.

4. **Calculate the Profit**:
The profit made by selling 800 grams at the selling price of ₹900 is:
\[ \text{Profit} = SP - CP \text{ of } 800 \text{ grams} = 900 - 800 = ₹100 \]

**Hint**: Profit is the difference between the selling price and the cost price of the quantity sold.

5. **Calculate the Profit Percentage**:
The profit percentage can be calculated using the formula:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{CP of 800 grams}}\right) \times 100 = \left(\frac{100}{800}\right) \times 100 = 12.5\% \]

**Hint**: To find the profit percentage, divide the profit by the cost price and then multiply by 100.

### Final Answer:
The profit percentage of the dishonest dealer is **12.5%**.