By selling an article for Rs. 100, on losses Rs. 10. Then, the loss per cent is -

Options

A. `(11)1/9%`
B. `(9)1/(11)%`
C. `10%`
D. None of these

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Identify the given values
- Selling Price (SP) = Rs. 100
- Loss = Rs. 10

**Hint:** Always start by identifying the values provided in the question.

### Step 2: Calculate the Cost Price (CP)
Since the selling price is less than the cost price due to the loss, we can find the cost price using the formula:
\[ \text{Cost Price (CP)} = \text{Selling Price (SP)} + \text{Loss} \]
Substituting the values:
\[ \text{CP} = 100 + 10 = 110 \text{ Rs.} \]

**Hint:** Remember that when there is a loss, the cost price is always greater than the selling price.

### Step 3: Calculate the Loss Percentage
The formula for calculating loss percentage is:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{Cost Price (CP)}} \right) \times 100 \]
Substituting the values:
\[ \text{Loss Percentage} = \left( \frac{10}{110} \right) \times 100 \]

### Step 4: Simplify the calculation
Now, we simplify the fraction:
\[ \frac{10}{110} = \frac{1}{11} \]
So,
\[ \text{Loss Percentage} = \left( \frac{1}{11} \right) \times 100 = \frac{100}{11} \]

### Step 5: Convert to mixed fraction
To convert \( \frac{100}{11} \) into a mixed fraction:
- 100 divided by 11 gives 9 with a remainder of 1.
Thus,
\[ \frac{100}{11} = 9 \frac{1}{11} \]

### Conclusion
The loss percentage is \( 9 \frac{1}{11} \% \).

**Final Answer:** The loss per cent is \( 9 \frac{1}{11} \% \).

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