A person sold an article at a loss of 8%. Had he sold it at a gain of 10.5%, he would have re-ceived rs 92.50 more. To gain 12%, he should have sold it for .

Options

A. rs 540.50
B. rs 560
C. rs 580
D. rs 537.40

Answer

To solve the problem step by step, we will use the information given in the question to find the cost price (CP) of the article and then determine the selling price (SP) required to achieve a 12% gain.

### Step 1: Define the variables
Let the cost price (CP) of the article be \( x \).

### Step 2: Calculate the selling price at a loss of 8%
When the article is sold at a loss of 8%, the selling price (SP) can be calculated as:
\[ SP = CP - (Loss\% \times CP) = x - (0.08 \times x) = 0.92x \]

### Step 3: Calculate the selling price at a gain of 10.5%
If the article were sold at a gain of 10.5%, the selling price would be:
\[ SP = CP + (Gain\% \times CP) = x + (0.105 \times x) = 1.105x \]

### Step 4: Set up the equation based on the information given
According to the problem, if the article were sold at a gain of 10.5%, he would have received Rs 92.50 more than when sold at a loss of 8%. Therefore, we can set up the equation:
\[ 1.105x = 0.92x + 92.50 \]

### Step 5: Solve the equation for \( x \)
Now, we will simplify and solve for \( x \):
\[ 1.105x - 0.92x = 92.50 \]
\[ 0.185x = 92.50 \]
\[ x = \frac{92.50}{0.185} = 500 \]

### Step 6: Calculate the selling price for a gain of 12%
To find the selling price required to achieve a gain of 12%, we use the formula:
\[ SP = CP + (Gain\% \times CP) = x + (0.12 \times x) = 1.12x \]
Substituting the value of \( x \):
\[ SP = 1.12 \times 500 = 560 \]

### Final Answer
To gain 12%, he should have sold it for Rs 560.

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