By selling a property for Rs 45000 a person incurs a loss of 10%. Find the selling price to gain the profit of 15 %?

Options

A. 58000
B. 57500
C. 60000
D. 55000

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the given information
We know that the selling price (SP) of the property is Rs. 45,000, and the person incurs a loss of 10%.

### Step 2: Calculate the Cost Price (CP)
To find the cost price when there is a loss, we can use the formula:
\[ CP = \frac{100}{100 - \text{Loss \%}} \times SP \]
Substituting the values:
\[ CP = \frac{100}{100 - 10} \times 45000 \]
\[ CP = \frac{100}{90} \times 45000 \]
\[ CP = \frac{10}{9} \times 45000 \]
\[ CP = 50000 \]
So, the cost price of the property is Rs. 50,000.

### Step 3: Determine the desired profit
Now, we want to find the selling price that would give a profit of 15%.

### Step 4: Calculate the Selling Price for a 15% profit
We can use the formula for selling price when there is a profit:
\[ SP = \frac{100 + \text{Profit \%}}{100} \times CP \]
Substituting the values:
\[ SP = \frac{100 + 15}{100} \times 50000 \]
\[ SP = \frac{115}{100} \times 50000 \]
\[ SP = 1.15 \times 50000 \]
\[ SP = 57500 \]
Thus, the selling price to gain a profit of 15% is Rs. 57,500.

### Final Answer
The selling price to gain a profit of 15% is Rs. 57,500.

---