A man sold two flats at the rate of Rs 574634 each.On one he gained 12% and on the other he lost 12%. His gain or loss percent in the whole transaction was.

Options

A. 1.44% gain
B. 1.44% gain
C. 1.44% loss
D. 2.56% loss

Answer

To solve the problem step by step, we will calculate the cost price (CP) of each flat based on the selling price (SP) and the gain/loss percentage.

### Step 1: Determine Selling Price (SP)
The selling price of each flat is given as Rs 574634.

### Step 2: Calculate Cost Price (CP) of Flat 1
Flat 1 has a gain of 12%.
Let the cost price of Flat 1 be \( CP_1 \).

Using the formula for selling price with gain:
\[ SP = CP + \text{Gain} \]
\[ SP = CP_1 + (12\% \text{ of } CP_1) = CP_1 + 0.12 \times CP_1 = 1.12 \times CP_1 \]
Thus, we can express the cost price as:
\[ CP_1 = \frac{SP}{1.12} = \frac{574634}{1.12} \approx 513,000 \]

### Step 3: Calculate Cost Price (CP) of Flat 2
Flat 2 has a loss of 12%.
Let the cost price of Flat 2 be \( CP_2 \).

Using the formula for selling price with loss:
\[ SP = CP - \text{Loss} \]
\[ SP = CP_2 - (12\% \text{ of } CP_2) = CP_2 - 0.12 \times CP_2 = 0.88 \times CP_2 \]
Thus, we can express the cost price as:
\[ CP_2 = \frac{SP}{0.88} = \frac{574634}{0.88} \approx 652,000 \]

### Step 4: Calculate Total Cost Price (CP)
Now, we can find the total cost price of both flats:
\[ \text{Total CP} = CP_1 + CP_2 = 513,000 + 652,000 = 1,165,000 \]

### Step 5: Calculate Total Selling Price (SP)
The total selling price of both flats is:
\[ \text{Total SP} = SP_1 + SP_2 = 574634 + 574634 = 1,149,268 \]

### Step 6: Calculate Total Gain or Loss
Now, we can find the total gain or loss:
\[ \text{Total Loss} = \text{Total CP} - \text{Total SP} = 1,165,000 - 1,149,268 = 15,732 \]

### Step 7: Calculate Loss Percentage
To find the loss percentage, we use the formula:
\[ \text{Loss Percentage} = \left(\frac{\text{Loss}}{\text{Total CP}}\right) \times 100 \]
\[ \text{Loss Percentage} = \left(\frac{15,732}{1,165,000}\right) \times 100 \approx 1.35\% \]

### Final Conclusion
The overall transaction results in a loss of approximately 1.35%.