A reduction of 25% in the price of rice enables a person to buy 10 kg more rice for 600. The reduced price per kg of rice is:

Options

A. 30
B. 25
C. 35
D. 15

Answer

To solve the problem step by step, we will follow the reasoning provided in the video transcript and break it down into clear steps.

### Step-by-Step Solution:

1. **Let the original price of rice per kg be \( x \).**
- This is our starting point where we define the variable for the original price.

2. **Calculate the reduced price after a 25% reduction.**
- The reduction of 25% means the new price will be:
\[ \text{New Price} = x - 0.25x = 0.75x = \frac{3x}{4} \]

3. **Determine how much rice can be bought at the original price and the reduced price.**
- At the original price \( x \), the amount of rice that can be bought for 600 is:
\[ \text{Rice at original price} = \frac{600}{x} \]
- At the reduced price \( \frac{3x}{4} \), the amount of rice that can be bought for 600 is:
\[ \text{Rice at reduced price} = \frac{600}{\frac{3x}{4}} = \frac{600 \times 4}{3x} = \frac{2400}{3x} \]

4. **Set up the equation based on the information given in the problem.**
- According to the problem, the difference in the amount of rice bought at the reduced price and the original price is 10 kg:
\[ \frac{2400}{3x} - \frac{600}{x} = 10 \]

5. **Simplify the equation.**
- To simplify, we can find a common denominator, which is \( 3x \):
\[ \frac{2400 - 1800}{3x} = 10 \]
- This simplifies to:
\[ \frac{600}{3x} = 10 \]

6. **Cross-multiply to solve for \( x \).**
- Cross-multiplying gives:
\[ 600 = 30x \]
- Dividing both sides by 30:
\[ x = \frac{600}{30} = 20 \]

7. **Calculate the reduced price.**
- Now that we have the original price \( x = 20 \), we can find the reduced price:
\[ \text{Reduced Price} = \frac{3x}{4} = \frac{3 \times 20}{4} = \frac{60}{4} = 15 \]

8. **Conclusion:**
- The reduced price per kg of rice is \( 15 \) rupees.

### Final Answer:
The reduced price per kg of rice is **15 rupees**.