A dealer gives as much discount (in per cent) as the markup (in per cent) above the cost price. What is the profit or loss per cent?

Options

A. `10%`
B. `1%`
C. `4%`
D. Can’t be determined

Answer

To solve the problem, we need to analyze the relationship between the cost price, markup, discount, and selling price. Let's break it down step by step.

### Step 1: Define the Cost Price
Let the cost price (CP) of the article be ₹100. This simplifies our calculations.

### Step 2: Define the Markup Percentage
Let the markup percentage be \( x\% \). Therefore, the marked price (MP) can be calculated as:
\[ \text{Marked Price (MP)} = \text{Cost Price} + \text{Markup} = 100 + \frac{x}{100} \times 100 = 100 + x \]

### Step 3: Define the Discount Percentage
According to the problem, the dealer gives a discount equal to the markup percentage. Thus, the discount is also \( x\% \). The selling price (SP) after applying the discount can be calculated as:
\[ \text{Selling Price (SP)} = \text{Marked Price} - \text{Discount} = (100 + x) - \frac{x}{100} \times (100 + x) \]
This can be simplified as:
\[ \text{SP} = (100 + x) - (x + \frac{x^2}{100}) = 100 + x - x - \frac{x^2}{100} = 100 - \frac{x^2}{100} \]

### Step 4: Calculate Profit or Loss
Now, we can find the profit or loss by comparing the selling price with the cost price:
\[ \text{Profit or Loss} = \text{SP} - \text{CP} = \left(100 - \frac{x^2}{100}\right) - 100 = -\frac{x^2}{100} \]
This indicates a loss since the result is negative.

### Step 5: Calculate the Loss Percentage
The loss percentage can be calculated using the formula:
\[ \text{Loss Percentage} = \left(\frac{\text{Loss}}{\text{Cost Price}}\right) \times 100 = \left(\frac{-\frac{x^2}{100}}{100}\right) \times 100 = -\frac{x^2}{100} \]
Since the loss percentage is dependent on \( x \), we cannot determine a specific value without knowing \( x \).

### Conclusion
Since the loss percentage varies based on the markup percentage \( x \), we conclude that the answer is:
**Can't be determined.**

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