The profit on selling an article for Rs 1,100 is equal to three times the amount of loss on selling it for Rs 700. To gain 12.5% the article must be sold for `:`

Options

A. Rs 787.50
B. Rs 877.50
C. Rs956
D. Rs 900

Answer

To solve the problem, we need to find the cost price (CP) of the article and then determine the selling price (SP) required to achieve a gain of 12.5%.

### Step-by-Step Solution:

1. **Understanding Profit and Loss:**
- Let the cost price of the article be \( CP \).
- When the article is sold for Rs. 1100, the profit is given by:
\[ \text{Profit} = SP - CP = 1100 - CP \]
- When the article is sold for Rs. 700, the loss is given by:
\[ \text{Loss} = CP - SP = CP - 700 \]

2. **Setting Up the Equation:**
- According to the problem, the profit on selling for Rs. 1100 is equal to three times the loss on selling for Rs. 700:
\[ 1100 - CP = 3(CP - 700) \]

3. **Expanding and Rearranging the Equation:**
- Expanding the right side:
\[ 1100 - CP = 3CP - 2100 \]
- Rearranging the equation:
\[ 1100 + 2100 = 3CP + CP \]
\[ 3200 = 4CP \]

4. **Calculating the Cost Price:**
- Dividing both sides by 4:
\[ CP = \frac{3200}{4} = 800 \]

5. **Calculating the Selling Price for a 12.5% Gain:**
- To find the selling price for a 12.5% gain, we first calculate 12.5% of the cost price:
\[ \text{Gain} = 12.5\% \text{ of } CP = \frac{12.5}{100} \times 800 = 100 \]
- Therefore, the selling price (SP) for a 12.5% gain is:
\[ SP = CP + \text{Gain} = 800 + 100 = 900 \]

6. **Final Answer:**
- The article must be sold for Rs. 900 to gain 12.5%.