A reductin of `10%` in the price of an article enables a dealer to purchase 25 articles more for Rs. 45000. What is the original price of the article ?

Options

A. Rs. 100
B. Rs. 150
C. Rs. 200
D. Rs. 250

Explanation

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

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

### Step 2: Calculate the Reduced Price
Since there is a reduction of 10% in the price, the new price after reduction will be:
\[ \text{Reduced Price} = x - \frac{10}{100} \cdot x = x - \frac{x}{10} = \frac{9x}{10} \]

### Step 3: Determine the Number of Articles Purchased
With the original price \( x \), the number of articles that could be purchased for Rs. 45000 is:
\[ \text{Number of Articles at Original Price} = \frac{45000}{x} \]
With the reduced price \( \frac{9x}{10} \), the number of articles that can be purchased is:
\[ \text{Number of Articles at Reduced Price} = \frac{45000}{\frac{9x}{10}} = \frac{45000 \cdot 10}{9x} = \frac{450000}{9x} \]

### Step 4: Set Up the Equation
According to the problem, the dealer can purchase 25 more articles after the price reduction. Therefore, we can set up the equation:
\[ \frac{450000}{9x} = \frac{45000}{x} + 25 \]

### Step 5: Simplify the Equation
To eliminate the fractions, multiply the entire equation by \( 9x \):
\[ 450000 = 9 \cdot 45000 + 25 \cdot 9x \]
This simplifies to:
\[ 450000 = 405000 + 225x \]

### Step 6: Solve for \( x \)
Now, isolate \( x \):
\[ 450000 - 405000 = 225x \]
\[ 45000 = 225x \]
\[ x = \frac{45000}{225} \]
\[ x = 200 \]

### Conclusion
The original price of the article is Rs. 200.

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