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?

### Concept & Cost Price Calculation To find the new profit or loss percentage, we first must find the original Cost Price (CP) of the house. The relationship between Cost Price, Selling Price (SP), and Profit Percentage is: $$ CP = \frac{SP \times 100}{100 + \text{Profit } \%} $$ ### Step-by-Step Solution * Given: SP of house = ₹ 6,30,000, Profit = $5\%$ * Calculate CP: $CP = \frac{630000}{1.05} = \frac{630000 \times 100}{105} = \text{₹ } 6,00,000$ * The original cost price of the house is ₹ 6,00,000. * New Given Scenario: Proposed New SP = ₹ 5,00,000. * Since New SP < CP, there is a loss. * Loss amount = $CP - \text{New SP} = 600000 - 500000 = \text{₹ } 1,00,000$. * Calculate Loss Percentage: $\text{Loss } \% = (\frac{\text{Loss}}{CP}) \times 100$ * $\text{Loss } \% = (\frac{100000}{600000}) \times 100 = \frac{100}{6}\%$ * Simplify the fraction: $\frac{100}{6}\% = \frac{50}{3}\% = 16 \frac{2}{3}\%$ ### Exam Strategy & Shortcut Notice the ratios directly. $105\%$ of CP = 6.3 L $1\%$ of CP = 6.3 L / 105 = 0.06 L CP = 6 L New SP is 5 L, which is 1 L less than CP. Loss fraction is $1/6$, and the standard percentage equivalent for $1/6$ is $16 \frac{2}{3}\%$. ### Common Pitfall Calculating the loss percentage on the new Selling Price instead of the original Cost Price. Always remember that profit and loss percentages are calculated on the Cost Price (CP) unless explicitly stated otherwise. ### Final Answer Therefore, the correct answer is **$16 \frac{2}{3}\%$ loss**.