If the discount is equal to one fifth of the marked price and the loss is half the discount then the percentage of loss is
यदि कटौती (बट्टा) अंकित मूल्य के 1/5 के बराबर हो और हानि कटौती से आधी हो, तो हानि का प्रतिशत है।

Options

A. A)10 `(1)/9%`
B. B)11 `(1)/9`%
C. C)`12 (1)/9%`
D. D)`13 (1)/9%`

Explanation

To solve the problem, we need to find the percentage of loss given that the discount is equal to one-fifth of the marked price and the loss is half the discount.

### Step-by-Step Solution:

1. **Let the Marked Price (MP) be denoted as \( MP \)**:
- According to the problem, the discount is one-fifth of the marked price.
- Therefore, the discount \( D = \frac{1}{5} \times MP \).

2. **Calculate the Selling Price (SP)**:
- The selling price can be calculated as:
\[ SP = MP - D \]
- Substituting the value of \( D \):
\[ SP = MP - \frac{1}{5} \times MP = \frac{4}{5} \times MP \]

3. **Determine the Loss**:
- The problem states that the loss is half of the discount.
- Therefore, the loss \( L = \frac{1}{2} \times D = \frac{1}{2} \times \frac{1}{5} \times MP = \frac{1}{10} \times MP \).

4. **Calculate the Cost Price (CP)**:
- The cost price can be calculated using the relationship between SP, CP, and Loss:
\[ CP = SP + L \]
- Substituting the values of \( SP \) and \( L \):
\[ CP = \frac{4}{5} \times MP + \frac{1}{10} \times MP \]
- To add these fractions, we need a common denominator:
\[ CP = \frac{8}{10} \times MP + \frac{1}{10} \times MP = \frac{9}{10} \times MP \]

5. **Calculate the Loss Percentage**:
- The loss percentage can be calculated using the formula:
\[ \text{Loss Percentage} = \left( \frac{L}{CP} \right) \times 100 \]
- Substituting the values of \( L \) and \( CP \):
\[ \text{Loss Percentage} = \left( \frac{\frac{1}{10} \times MP}{\frac{9}{10} \times MP} \right) \times 100 \]
- Simplifying this gives:
\[ \text{Loss Percentage} = \left( \frac{1}{9} \right) \times 100 = \frac{100}{9} \approx 11.11\% \]

### Final Answer:
The percentage of loss is \( 11 \frac{1}{9} \% \).

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