A shopkeeper sells an article at a loss of `12(1)/(2)%`. Had he sold it for Rs. `51.80` more than he would have earned a profit of `6%`. The cost price of the article is

Options

A. Rs. 280
B. Rs. 300
C. Rs. 380
D. Rs. 400

Answer

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

### Step 1: Understand the Loss and Profit Percentages
The shopkeeper sells the article at a loss of \(12.5\%\). This means that the selling price (SP) is \(87.5\%\) of the cost price (CP).

### Step 2: Set Up the Equations
Let the cost price be \(X\).
- Selling Price at a loss of \(12.5\%\):
\[ SP = X - \left(\frac{12.5}{100} \times X\right) = 0.875X \]

If he had sold it for Rs. \(51.80\) more, he would have made a profit of \(6\%\). This means the new selling price would be \(106\%\) of the cost price:
- Selling Price at a profit of \(6\%\):
\[ SP' = X + \left(\frac{6}{100} \times X\right) = 1.06X \]

### Step 3: Relate the Two Selling Prices
According to the problem, the difference between the new selling price and the current selling price is Rs. \(51.80\):
\[ 1.06X - 0.875X = 51.80 \]

### Step 4: Simplify the Equation
Now, simplify the left side:
\[ (1.06 - 0.875)X = 51.80 \]
\[ 0.185X = 51.80 \]

### Step 5: Solve for Cost Price (X)
To find \(X\), divide both sides by \(0.185\):
\[ X = \frac{51.80}{0.185} \]

Calculating this gives:
\[ X = 280 \]

### Conclusion
The cost price of the article is Rs. \(280\).

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