By selling a plot of land for Rs. 45,000 a person loses 10%. At what price should he sell it to gain 15%?

Options

A. Rs. 50,000
B. Rs. 55,000
C. Rs. 57.500
D. Rs. 60,000

Answer

To solve the problem step by step, we need to find out the cost price (CP) of the plot of land first and then determine the selling price (SP) required to achieve a 15% profit.

### Step 1: Determine the Cost Price (CP)
Given that selling the plot for Rs. 45,000 results in a loss of 10%, we can express this mathematically.

Let the Cost Price (CP) be \( x \).

Since there is a loss of 10%, the Selling Price (SP) can be calculated as:
\[ SP = CP - (10\% \text{ of } CP) = CP - 0.1 \times CP = 0.9 \times CP \]

From the problem, we know that:
\[ 0.9 \times CP = 45,000 \]

To find the Cost Price (CP), we can rearrange the equation:
\[ CP = \frac{45,000}{0.9} \]
Calculating this gives:
\[ CP = 50,000 \]

### Step 2: Calculate the Selling Price for a 15% Gain
Now that we have the Cost Price, we need to calculate the Selling Price (SP) that would yield a 15% profit.

The Selling Price for a 15% gain can be calculated as:
\[ SP = CP + (15\% \text{ of } CP) = CP + 0.15 \times CP = 1.15 \times CP \]

Substituting the value of CP we found:
\[ SP = 1.15 \times 50,000 \]
Calculating this gives:
\[ SP = 57,500 \]

### Conclusion
Therefore, the price at which he should sell the plot of land to gain 15% is Rs. 57,500.

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