A dishonest dealer sells articles at 10% loss on cost price but uses the weight of 16 g instead of 18 g. What is his profit or loss per cent?

Options

A. `1(1)/(4)% ` gain
B. `1(1)/(4)%` gain
C. `3(1)/(4)%` loss
D. `6(1)/(4)%` gain

Answer

To solve the problem step by step, we will analyze the situation of the dishonest dealer who claims to sell at a 10% loss but uses incorrect weights.

### Step 1: Understand the Cost Price (CP) and Selling Price (SP)
Let’s assume the cost price (CP) of 18 grams of the article is ₹18.

### Step 2: Calculate the Selling Price (SP) at 10% Loss
Since the dealer claims to sell at a 10% loss, we can find the selling price (SP) using the formula:
\[ SP = CP - (10\% \text{ of } CP) \]
Calculating this:
\[ SP = 18 - (0.10 \times 18) = 18 - 1.8 = ₹16.2 \]

### Step 3: Identify the Actual Weight Sold
The dealer uses a weight of 16 grams instead of 18 grams. Therefore, when he sells at the price of 18 grams, he is actually selling only 16 grams.

### Step 4: Calculate the Cost Price of 16 grams
Since the cost price of 18 grams is ₹18, the cost price (CP) of 16 grams can be calculated as:
\[ CP \text{ of 16 grams} = \left(\frac{16}{18}\right) \times 18 = ₹16 \]

### Step 5: Calculate the Profit
Now we can find the profit made by the dealer:
\[ \text{Profit} = SP - CP \text{ of 16 grams} \]
Calculating this:
\[ \text{Profit} = 16.2 - 16 = ₹0.2 \]

### Step 6: Calculate the Profit Percentage
To find the profit percentage, we use the formula:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{CP of 16 grams}}\right) \times 100 \]
Calculating this:
\[ \text{Profit Percentage} = \left(\frac{0.2}{16}\right) \times 100 = 1.25\% \]

### Conclusion
The dishonest dealer makes a profit of **1.25%**.

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