An article is sold at a profit of 15%. If both the cost price and the selling price of the article are reduced by Rs. 140 each then the profit percentage becomes 19.2%. The cost price of the article is:

Options

A. Rs. 560
B. Rs. 720
C. Rs. 680
D. Rs. 640

Answer

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

### Step 1: Define Variables
Let the cost price of the article be \( x \).

### Step 2: Calculate Selling Price
Since the article is sold at a profit of 15%, the selling price (SP) can be calculated as:
\[ SP = CP + 15\% \text{ of } CP = x + 0.15x = 1.15x \]

### Step 3: Adjust Cost Price and Selling Price
According to the problem, both the cost price and the selling price are reduced by Rs. 140 each. Therefore, the new cost price and selling price will be:
\[ \text{New CP} = x - 140 \]
\[ \text{New SP} = 1.15x - 140 \]

### Step 4: Set Up the New Profit Percentage Equation
The new profit percentage is given as 19.2%. The formula for profit percentage is:
\[ \text{Profit Percentage} = \frac{\text{Profit}}{\text{Cost Price}} \times 100 \]
Here, the profit can be expressed as:
\[ \text{Profit} = \text{New SP} - \text{New CP} = (1.15x - 140) - (x - 140) = 1.15x - 140 - x + 140 = 0.15x \]
Now, substituting into the profit percentage formula:
\[ 19.2 = \frac{0.15x}{x - 140} \times 100 \]

### Step 5: Simplify the Equation
To eliminate the percentage, we can rewrite the equation:
\[ 19.2 = \frac{0.15x}{x - 140} \times 100 \implies 0.192 = \frac{0.15x}{x - 140} \]
Cross-multiplying gives:
\[ 0.192(x - 140) = 0.15x \]

### Step 6: Expand and Rearrange the Equation
Expanding the left side:
\[ 0.192x - 26.88 = 0.15x \]
Now, rearranging the equation:
\[ 0.192x - 0.15x = 26.88 \]
\[ 0.042x = 26.88 \]

### Step 7: Solve for x
Now, divide both sides by 0.042:
\[ x = \frac{26.88}{0.042} = 640 \]

### Conclusion
Thus, the cost price of the article is:
\[ \text{Cost Price (CP)} = 640 \]