An articale was sold at a loss of 12%. If it was sold for Rs 630 more, then there would have been a gain of 6%. Find the cost price of the article.

Options

A. Rs 3,500
B. Rs 2,800
C. Rs 2,500
D. Rs 3,000

Answer

To solve the problem step by step, we will define the cost price (CP) of the article and then calculate the selling prices (SP) based on the given loss and gain percentages.

### Step 1: Define the Cost Price
Let the cost price (CP) of the article be Rs 100 (we will scale this later).

### Step 2: Calculate Selling Price at Loss
Since the article is sold at a loss of 12%, we can calculate the selling price (SP1) as follows:
\[ SP1 = CP - \text{Loss} = 100 - 12\% \text{ of } 100 = 100 - 12 = Rs 88 \]

### Step 3: Calculate Selling Price at Gain
If the article were sold for Rs 630 more, there would be a gain of 6%. Thus, we can calculate the selling price (SP2) as follows:
\[ SP2 = CP + \text{Gain} = 100 + 6\% \text{ of } 100 = 100 + 6 = Rs 106 \]

### Step 4: Set Up the Equation
According to the problem, the difference between the two selling prices (SP2 - SP1) is Rs 630:
\[ SP2 - SP1 = 630 \]
Substituting the values we found:
\[ 106 - 88 = 630 \]
This simplifies to:
\[ 18 = 630 \]

### Step 5: Solve for Cost Price
Now we need to find the actual cost price (CP) based on the Rs 100 we initially assumed:
\[ \text{Let the actual CP be } x. \]
From the equation we derived:
\[ 18\% \text{ of } x = 630 \]
This means:
\[ \frac{18}{100} \times x = 630 \]
To find x, we rearrange the equation:
\[ x = 630 \times \frac{100}{18} \]
Calculating this gives:
\[ x = 630 \times \frac{100}{18} = 630 \times 5.555... \approx 3500 \]

### Final Answer
Thus, the cost price of the article is Rs 3500.

---