By selling 50 pens, a shopkeeper lost the amount equal to the selling price of 10 pens. His loss per cent is __________.

Answer

To find the loss percentage of the shopkeeper who sold 50 pens and incurred a loss equal to the selling price of 10 pens, we can follow these steps:

### Step 1: Define Variables
Let the selling price (SP) of one pen be \( x \).

### Step 2: Calculate Total Selling Price
The total selling price (SP) of 50 pens is:
\[ \text{Total SP} = 50 \times x = 50x \]

### Step 3: Calculate Loss Amount
According to the problem, the loss incurred by the shopkeeper is equal to the selling price of 10 pens:
\[ \text{Loss} = \text{SP of 10 pens} = 10 \times x = 10x \]

### Step 4: Calculate Cost Price
Using the relationship between Cost Price (CP), Selling Price (SP), and Loss:
\[ \text{CP} = \text{SP} + \text{Loss} \]
Substituting the values we have:
\[ \text{CP} = 50x + 10x = 60x \]

### Step 5: Calculate Loss Percentage
The formula for loss percentage is:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{CP}} \right) \times 100 \]
Substituting the values we found:
\[ \text{Loss Percentage} = \left( \frac{10x}{60x} \right) \times 100 \]

### Step 6: Simplify the Expression
The \( x \) in the numerator and denominator cancels out:
\[ \text{Loss Percentage} = \left( \frac{10}{60} \right) \times 100 = \frac{1}{6} \times 100 \]

### Step 7: Final Calculation
Calculating \( \frac{1}{6} \times 100 \):
\[ \text{Loss Percentage} = 16.67\% \]

Thus, the loss percentage is \( 16.67\% \).

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