A property dealer sells a house for Rs.9,00,000 and in the bargain makes `12.5 %` Had he sold it for Rs. 6,00,000, then what percentage of loss or gain have made ?

Options

A. `25 %` loss
B. `10%` loss
C. `12 (1)/(2)%` gain
D. None of these

Answer

To solve the problem step by step, we need to first determine the cost price of the house based on the selling price and the profit percentage. Then we will calculate the loss percentage if the house is sold for a different amount.

### Step-by-Step Solution:

1. **Identify the Selling Price and Profit Percentage**:
- Selling Price (SP) = Rs. 9,00,000
- Profit Percentage = 12.5%

2. **Calculate the Cost Price (CP)**:
- Let the Cost Price be \( X \).
- Profit = \( 12.5\% \) of Cost Price = \( \frac{12.5}{100} \times X = \frac{1}{8} X \).
- Therefore, Selling Price can be expressed as:
\[ SP = CP + Profit \implies 9,00,000 = X + \frac{1}{8}X \]
- Combining the terms:
\[ 9,00,000 = \frac{8}{8}X + \frac{1}{8}X = \frac{9}{8}X \]
- To find \( X \), multiply both sides by \( \frac{8}{9} \):
\[ X = 9,00,000 \times \frac{8}{9} = 8,00,000 \]
- Thus, the Cost Price (CP) is Rs. 8,00,000.

3. **Calculate Loss when Selling Price is Rs. 6,00,000**:
- New Selling Price (SP) = Rs. 6,00,000
- Since the Selling Price is less than the Cost Price, there is a loss.
- Loss = Cost Price - Selling Price = \( 8,00,000 - 6,00,000 = 2,00,000 \).

4. **Calculate the Loss Percentage**:
- Loss Percentage = \( \frac{Loss}{Cost Price} \times 100 \)
- Substituting the values:
\[ Loss\% = \frac{2,00,000}{8,00,000} \times 100 \]
- Simplifying the fraction:
\[ Loss\% = \frac{2}{8} \times 100 = \frac{1}{4} \times 100 = 25\% \]

### Final Answer:
The percentage of loss if the house is sold for Rs. 6,00,000 is **25%**.