A property dealer sells a house for Rs. 6,30,000 and in the bargain makes a profit of 5%. Had he sold it for Rs. 5,00,000, then what percentage of loss or gain he would have made?

Options

A. `2 (1)/(4) %` gain
B. `10%` loss
C. `12 (1)/(2)%` loss
D. `16 (2)/(3)%` loss

Answer

To solve the problem step by step, we need to determine the cost price (CP) of the house first, and then calculate the loss percentage when the house is sold for Rs. 5,00,000.

### Step 1: Calculate the Cost Price (CP)
Given that the selling price (SP) of the house is Rs. 6,30,000 and the profit made is 5%, we can use the formula for SP in terms of CP and profit percentage:

\[ SP = CP + \text{Profit} \]

Since the profit is 5% of CP, we can express it as:

\[ SP = CP + 0.05 \times CP = 1.05 \times CP \]

Now, substituting the value of SP:

\[ 6,30,000 = 1.05 \times CP \]

To find CP, we rearrange the equation:

\[ CP = \frac{6,30,000}{1.05} \]

Calculating this gives:

\[ CP = 6,00,000 \]

### Step 2: Calculate the Loss when Sold for Rs. 5,00,000
Now, if the house is sold for Rs. 5,00,000, we need to find out the loss incurred:

\[ \text{Loss} = CP - SP \]

Substituting the values we have:

\[ \text{Loss} = 6,00,000 - 5,00,000 = 1,00,000 \]

### Step 3: Calculate the Loss Percentage
The loss percentage can be calculated using the formula:

\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{CP} \right) \times 100 \]

Substituting the values:

\[ \text{Loss Percentage} = \left( \frac{1,00,000}{6,00,000} \right) \times 100 \]

Calculating this gives:

\[ \text{Loss Percentage} = \frac{1}{6} \times 100 = 16.67\% \]

### Final Answer
Thus, the percentage of loss when the house is sold for Rs. 5,00,000 is approximately **16.67%**.

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