An article was sold at a loss of 12% If it was sold for Rs. 360 more, then there would have been a gain of 6%. Find the cost price of the article.

Options

A. Rs. 3,500
B. Rs. 2,000
C. Rs. 2,500
D. Rs. 3,000

Answer

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

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

### Step 2: Calculate Selling Price at Loss
Since the article was sold at a loss of 12%, the selling price (SP) at this loss can be calculated as:
\[ SP_{loss} = CP - (12\% \text{ of } CP) = x - 0.12x = 0.88x \]

### Step 3: Calculate Selling Price at Gain
If the article was sold for Rs. 360 more, it would have resulted in a gain of 6%. Therefore, the selling price at this gain can be calculated as:
\[ SP_{gain} = CP + (6\% \text{ of } CP) = x + 0.06x = 1.06x \]

### Step 4: Set Up the Equation
According to the problem, the difference between the selling price at gain and the selling price at loss is Rs. 360. Therefore, we can set up the equation:
\[ SP_{gain} - SP_{loss} = 360 \]
Substituting the values we calculated:
\[ 1.06x - 0.88x = 360 \]

### Step 5: Simplify the Equation
Now, simplify the left side:
\[ (1.06 - 0.88)x = 360 \]
\[ 0.18x = 360 \]

### Step 6: Solve for x
To find \( x \), divide both sides by 0.18:
\[ x = \frac{360}{0.18} = 2000 \]

### Step 7: Conclusion
Thus, the cost price of the article is:
\[ \text{Cost Price} = Rs. 2000 \]

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