A trader marked the selling price of an artcle at 10% above the cost price. At the time of selling, he allows certain discount and suffers a loss of 1%. He allowed the discount of :

Options

A. `11%`
B. `10%`
C. `9%`
D. `10.5%`

Answer

To solve the problem step by step, we will follow the given information about the cost price, selling price, and the discount allowed by the trader.

### Step 1: Define the Cost Price (CP)
Let the cost price (CP) of the article be \( x \).

### Step 2: Calculate the Marked Selling Price (SP)
The trader marks the selling price at 10% above the cost price. Therefore, the marked selling price (MSP) can be calculated as:
\[ \text{MSP} = \text{CP} + 10\% \text{ of CP} = x + 0.1x = 1.1x \]

### Step 3: Determine the Selling Price after Discount
The trader allows a certain discount on the marked selling price, which results in a loss of 1%. This means the selling price (SP) after the discount is:
\[ \text{SP} = \text{CP} - 1\% \text{ of CP} = x - 0.01x = 0.99x \]

### Step 4: Set Up the Equation for Discount
Let the discount be \( d \). The selling price after applying the discount can be expressed as:
\[ \text{SP} = \text{MSP} - d \]
Substituting the values we have:
\[ 0.99x = 1.1x - d \]

### Step 5: Solve for Discount
Rearranging the equation to find \( d \):
\[ d = 1.1x - 0.99x = 0.11x \]

### Step 6: Calculate the Discount Percentage
To find the discount percentage, we calculate:
\[ \text{Discount Percentage} = \left( \frac{d}{\text{MSP}} \right) \times 100 = \left( \frac{0.11x}{1.1x} \right) \times 100 \]
This simplifies to:
\[ \text{Discount Percentage} = \left( \frac{0.11}{1.1} \right) \times 100 = 10\% \]

### Final Answer
The discount allowed by the trader is **10%**.

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