A person sold an article at a loss. of 8%. Had he sold it at a gain of 10.5%, he would have received 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.537.44

Answer

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

### Step 1: Understand the given information
The person sold an article at a loss of 8%. If he had sold it at a gain of 10.5%, he would have received Rs. 92.50 more.

### Step 2: Define the Cost Price (CP)
Let the Cost Price (CP) of the article be Rs. 100 (this simplifies calculations).

### Step 3: Calculate the Selling Price (SP) at 8% loss
If the CP is Rs. 100 and he sells it at a loss of 8%, the Selling Price (SP) can be calculated as:
\[ SP = CP - (Loss\% \times CP) = 100 - (8\% \times 100) = 100 - 8 = Rs. 92 \]

### Step 4: Calculate the Selling Price (SP) at 10.5% gain
If he had sold it at a gain of 10.5%, the Selling Price would be:
\[ SP = CP + (Gain\% \times CP) = 100 + (10.5\% \times 100) = 100 + 10.5 = Rs. 110.5 \]

### Step 5: Set up the equation based on the difference in Selling Prices
According to the problem, the difference between the Selling Price at 10.5% gain and the Selling Price at 8% loss is Rs. 92.50:
\[ 110.5 - 92 = 92.5 \]
This confirms our calculations so far.

### Step 6: Calculate the Cost Price (CP) using the difference
We know that the difference of Rs. 92.50 corresponds to an increase of 18.5% (10.5% gain - (-8% loss)):
\[ 18.5\% \text{ of CP} = 92.5 \]
Let CP = x. Then:
\[ 0.185x = 92.5 \]
To find x (the actual CP):
\[ x = \frac{92.5}{0.185} = Rs. 500 \]

### Step 7: Calculate the Selling Price (SP) for a 12% gain
To find the Selling Price for a 12% gain, we calculate:
\[ SP = CP + (Gain\% \times CP) = 500 + (12\% \times 500) = 500 + 60 = Rs. 560 \]

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

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