A dishonest dealer sells his goods at 10% loss on cost price but uses 20% less weight. What is his profit or loss per cent?

Options

A. 12% loss
B. 22.5% gain
C. 13.9% loss
D. 12.5% gain

Answer

To solve the problem step by step, we will analyze the situation involving the dishonest dealer who sells goods at a loss while using less weight.

### Step 1: Understand the Problem
The dealer claims to sell 1000 grams of goods but actually sells only 800 grams due to using 20% less weight. He also sells these goods at a 10% loss on the cost price.

### Step 2: Assume a Cost Price
Let's assume the cost price (CP) of 1000 grams of goods is ₹1000.

### Step 3: Calculate the Actual Weight Sold
Since the dealer uses 20% less weight, the actual weight he sells is:
\[ \text{Actual weight} = 1000 \text{ grams} - (20\% \text{ of } 1000 \text{ grams}) = 1000 \text{ grams} - 200 \text{ grams} = 800 \text{ grams} \]

### Step 4: Calculate the Cost Price of the Actual Weight Sold
The cost price of 800 grams can be calculated as follows:
\[ \text{CP of 800 grams} = \left(\frac{800}{1000}\right) \times 1000 = ₹800 \]

### Step 5: Calculate the Selling Price
The dealer sells at a 10% loss on the cost price of 1000 grams. Therefore, the selling price (SP) can be calculated as:
\[ \text{SP} = \text{CP} - \text{Loss} = 1000 - (10\% \text{ of } 1000) = 1000 - 100 = ₹900 \]

### Step 6: Calculate the Profit or Loss
Now, we can determine the profit or loss:
\[ \text{Profit or Loss} = \text{SP} - \text{CP of actual weight sold} = 900 - 800 = ₹100 \]

### Step 7: Calculate the Profit Percentage
To find the profit percentage, we use the formula:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{CP of actual weight sold}}\right) \times 100 = \left(\frac{100}{800}\right) \times 100 = 12.5\% \]

### Final Answer
The dealer makes a profit of **12.5%**.

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