If a trader estimates his loss as 10% of the selling price, what is his real loss percent?

Options

A. `(100)/(8)%`
B. `(100)/(11)%`
C. `(100)/(13)%`
D. `(100)/(7)%`

Explanation

To find the real loss percent when a trader estimates his loss as 10% of the selling price, we can follow these steps:

### Step 1: Understand the relationship between Cost Price (CP), Selling Price (SP), and Loss
The loss can be defined as:
\[ \text{Loss} = \text{Cost Price} - \text{Selling Price} \quad (CP - SP) \]
The loss percentage is calculated based on the selling price:
\[ \text{Loss Percentage} = \left( \frac{CP - SP}{SP} \right) \times 100 \]

### Step 2: Set up the equation based on the given loss percentage
Given that the trader estimates his loss as 10% of the selling price, we can set up the equation:
\[ \frac{CP - SP}{SP} = \frac{10}{100} \quad \text{(which simplifies to)} \quad \frac{CP - SP}{SP} = \frac{1}{10} \]

### Step 3: Express CP in terms of SP
From the equation above, we can rearrange it:
\[ CP - SP = \frac{1}{10} \times SP \]
This implies:
\[ CP = SP + \frac{1}{10} \times SP = \frac{10}{10} \times SP + \frac{1}{10} \times SP = \frac{11}{10} \times SP \]

### Step 4: Substitute a value for SP to find CP
Let's assume \( SP = 10 \) (this is an arbitrary choice to simplify calculations):
\[ CP = \frac{11}{10} \times 10 = 11 \]

### Step 5: Calculate the actual loss
Now, we can find the actual loss:
\[ \text{Loss} = CP - SP = 11 - 10 = 1 \]

### Step 6: Calculate the real loss percentage
The real loss percentage is calculated based on the cost price:
\[ \text{Real Loss Percentage} = \left( \frac{CP - SP}{CP} \right) \times 100 = \left( \frac{1}{11} \right) \times 100 \]
Calculating this gives:
\[ \text{Real Loss Percentage} = \frac{100}{11} \approx 9.09\% \]

### Final Answer
The real loss percentage is approximately **9.09%**.

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