A reduction of 25% in the price of an article enables a man to buy 50 kilograms more for Rs 500. What is the reduced price per kilogram?

Options

A. 3
B. `2.50`
C. `2.05`
D. `2.40`

Answer

To solve the problem step by step, we will follow the reasoning outlined in the video transcript.

### Step-by-Step Solution:

1. **Define the Original Price**:
Let the original price per kilogram of the article be Rs. \( x \).

2. **Calculate the Reduced Price**:
Since there is a reduction of 25%, the reduced price per kilogram will be:
\[ \text{Reduced Price} = x - \frac{25}{100} \times x = x - \frac{x}{4} = \frac{3x}{4} \]

3. **Calculate the Quantity Bought at Original Price**:
The quantity of the article that can be bought for Rs. 500 at the original price is:
\[ \text{Quantity at Original Price} = \frac{500}{x} \]

4. **Calculate the Quantity Bought at Reduced Price**:
The quantity of the article that can be bought for Rs. 500 at the reduced price is:
\[ \text{Quantity at Reduced Price} = \frac{500}{\frac{3x}{4}} = \frac{500 \times 4}{3x} = \frac{2000}{3x} \]

5. **Set Up the Equation**:
According to the problem, the difference in quantity bought at the reduced price compared to the original price is 50 kg:
\[ \frac{2000}{3x} - \frac{500}{x} = 50 \]

6. **Find a Common Denominator**:
The common denominator for the fractions is \( 3x \). Rewriting the equation:
\[ \frac{2000}{3x} - \frac{1500}{3x} = 50 \]
This simplifies to:
\[ \frac{2000 - 1500}{3x} = 50 \]
\[ \frac{500}{3x} = 50 \]

7. **Cross-Multiply to Solve for \( x \)**:
Cross-multiplying gives:
\[ 500 = 50 \times 3x \]
\[ 500 = 150x \]
Dividing both sides by 150:
\[ x = \frac{500}{150} = \frac{10}{3} \]

8. **Calculate the Reduced Price**:
Now substitute \( x \) back into the reduced price formula:
\[ \text{Reduced Price} = \frac{3x}{4} = \frac{3 \times \frac{10}{3}}{4} = \frac{10}{4} = 2.5 \]

### Final Answer:
The reduced price per kilogram is Rs. 2.50.