On selling an article for Rs. 115, the gain is 20% more than the loss incurred on selling it for Rs. 104. If the article is sold for Rs. 130.80, then the profit percentage is:

Options

A. 25
B. 18
C. 30
D. 20

Answer

To solve the problem, we need to find the cost price (CP) of the article and then calculate the profit percentage when it is sold for Rs. 130.80.

### Step-by-step Solution:

1. **Let the Cost Price be X**:
We denote the cost price of the article as X.

2. **Calculate Profit and Loss**:
- Selling Price (SP) when sold for Rs. 115:
- Profit = SP - CP = 115 - X
- Selling Price (SP) when sold for Rs. 104:
- Loss = CP - SP = X - 104

3. **Set Up the Equation**:
According to the problem, the profit when sold for Rs. 115 is 20% more than the loss when sold for Rs. 104:
\[ 115 - X = 1.2 \times (X - 104) \]

4. **Expand and Rearrange the Equation**:
\[ 115 - X = 1.2X - 124.8 \]
Rearranging gives:
\[ 115 + 124.8 = 1.2X + X \]
\[ 239.8 = 2.2X \]

5. **Solve for X**:
\[ X = \frac{239.8}{2.2} = 109 \]

6. **Calculate Profit when sold for Rs. 130.80**:
- Profit = Selling Price - Cost Price:
\[ \text{Profit} = 130.80 - 109 = 21.80 \]

7. **Calculate Profit Percentage**:
Profit percentage is calculated as:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 \]
Substituting the values:
\[ \text{Profit Percentage} = \left( \frac{21.80}{109} \right) \times 100 \approx 20\% \]

### Final Answer:
The profit percentage when the article is sold for Rs. 130.80 is **20%**.