A shopkeepers sells an article at `12 (1)/(2)` % loss. If he sells it for Rs. 92.50 more, then he gains 6%. What is the cost price of the article?

Options

A. Rs. 510
B. Rs. 500
C. Rs. 575
D. Rs. 600

Answer

To find the cost price of the article, we can follow these steps:

### Step 1: Understand the Loss and Gain Percentages
The shopkeeper sells the article at a loss of 12.5%. If he sells it for Rs. 92.50 more, he gains 6%.

### Step 2: Calculate the Effective Change in Price
The total change in price when moving from a 12.5% loss to a 6% gain is:
- Loss of 12.5% means the selling price is 87.5% of the cost price.
- Gain of 6% means the selling price is 106% of the cost price.

The difference between these two percentages is:
\[ 106\% - 87.5\% = 18.5\% \]

### Step 3: Set Up the Equation
Let the cost price be \( CP \). According to the problem, the difference in selling price due to the change in percentage is equal to Rs. 92.50. Therefore, we can write the equation as:
\[ 18.5\% \text{ of } CP = 92.50 \]

### Step 4: Convert Percentage to Decimal
To express 18.5% as a decimal, we divide by 100:
\[ 18.5\% = \frac{18.5}{100} = 0.185 \]

### Step 5: Substitute and Solve for CP
Now we can substitute this into our equation:
\[ 0.185 \times CP = 92.50 \]

To find \( CP \), divide both sides by 0.185:
\[ CP = \frac{92.50}{0.185} \]

### Step 6: Calculate the Cost Price
Now, we perform the calculation:
\[ CP = \frac{92.50}{0.185} \approx 500 \]

Thus, the cost price of the article is Rs. 500.

### Final Answer
The cost price of the article is Rs. 500.

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