Question

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

• A. \(2\frac{1}{4}\%\) gain
• B. 10% loss
• C. \(12\frac{1}{2}\%\) loss
• D. \(16\frac{2}{3}\%\) loss

Answer 1

The Correct Option is D

Let the cost price (CP) of the house be \( x \). According to the problem, the house is sold for ₹6,30,000 with a 5% profit. We can use the formula for selling price (SP) when profit is involved:

\[ \text{SP} = \text{CP} \times \left(1 + \frac{\text{Profit \%}}{100}\right) \]

Given \( \text{SP} = 6,30,000 \) and \(\text{Profit \%} = 5\),

\[ 6,30,000 = x \times \left(1 + \frac{5}{100}\right) \]

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

Solve for \( x \) (CP):

\[ x = \frac{6,30,000}{1.05} = 6,00,000 \]

If the house is sold for ₹5,00,000, calculate the profit or loss percent using:

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

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

This indicates a loss of ₹1,00,000. Now, find the percentage loss:

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

\[ \text{Loss \%} = \left( \frac{1,00,000}{6,00,000} \right) \times 100 = 16.67\% \]

Thus, the loss percentage is \(16 \frac{2}{3}\% \). Therefore, the correct answer is \(16 \frac{2}{3}\%\) loss.