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The text from the image reads:

"एक व्यक्ति प्रतिदिन 9 घंटे विश्राम करके एक निश्चित दूरी 50 दिन में तय कर लेता है। यदि वह दुगुना आराम करे, दुगुना तेज चले, तब वह दुगुनी दूरी कितने दिन में तय करेगा?"

Translation: 
A person covers a certain distance by resting for 9 hours daily in 50 days. If he doubles his rest time and doubles his walking speed, in how many days will he cover double the distance?

### Solution approach:

1. **Original case**:
   - The person covers the distance in 50 days with 9 hours of rest.
   - This means he is walking for \(24 - 9 = 15\) hours a day.
   
2. **New case**:
   - He doubles his rest time, meaning now he rests for \(9 \times 2 = 18\) hours.
   - Hence, he will walk for \(24 - 18 = 6\) hours a day.
   - Also, he doubles his walking speed, so he covers twice the distance in the same amount of time.
   
3. **Comparison**:
   - In the original case, he walked for 15 hours a day at a normal speed.
   - Now, he walks for 6 hours a day but at double speed. So, the effective distance covered per day is the same as walking 12 hours at normal speed.

4. **Distance and Time**:
   - Originally, he covered the distance in 50 days.
   - Now, his effective walking time is \(12/15\) of the original (since he now walks for an equivalent of 12 hours instead of 15).
   - Therefore, the time required to cover double the distance would be:

   \[
   \text{New time} = \frac{50 \times 2}{12/15} = 50 \times 2 \times \frac{15}{12} = 125 \text{ days}.
   \]

So, he will cover the double distance in **125 days**.

Would you like more details or have any questions?

Here are 5 related questions for practice:
1. What would be the new time if the person triples his rest but maintains his original walking speed?
2. How much distance would the person cover if he rests for only 6 hours daily at the original speed?
3. If the person rests for 12 hours a day but triples his walking speed, how many days will it take to cover the original distance?
4. What if the walking speed is halved and rest time remains the same—how many days will it take to cover the original distance?
5. Can we generalize a formula for time based on varying rest and speed ratios?

**Tip**: Always compare effective walking time per day to determine the total time for new conditions.

एक व्यक्ति प्रतिदिन 9 घंटे विश्राम करके एक निश्चित दूरी 50 दिन में तय कर लेता है। यदि वह दुगुना आराम करे, दुगुना तेज चले, तब वह दुगुनी दूरी कितने दिन में तय करेगा?

Learn how to solve a problem involving time, speed, and distance where a person doubles both rest time and walking speed. This solution helps understand effective time and speed relationships, suitable for students in Grades 7-9.

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