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The question in the image is in Hindi. Here's the translated version:

**Question:**  
Two runners A and B run on an 800-meter-long circular track. They both complete 18 rounds in 200 seconds and 250 seconds respectively. After how much time will the faster runner overtake the slower runner for the last time?

**Answer Options:**
1. 2700 seconds
2. 4000 seconds
3. 2250 seconds
4. 1800 seconds

**Solution:**

To solve this, we first need to calculate the speeds of runners A and B:

1. **Speed Calculation:**
   - Runner A completes 18 rounds in 200 seconds.
     \[
     \text{Speed of A} = \frac{\text{Distance}}{\text{Time}} = \frac{18 \times 800}{200} = 72 \text{ meters/second}
     \]
   - Runner B completes 18 rounds in 250 seconds.
     \[
     \text{Speed of B} = \frac{\text{Distance}}{\text{Time}} = \frac{18 \times 800}{250} = 57.6 \text{ meters/second}
     \]

2. **Relative Speed:**
   - Relative speed between A and B:
     \[
     \text{Relative Speed} = 72 - 57.6 = 14.4 \text{ meters/second}
     \]

3. **Time to meet again on a circular track (LCM calculation):**
   - We find the Least Common Multiple (LCM) of the time taken by A and B to complete one round:
     - Time taken by A to complete one round: \(\frac{800}{72}\) seconds.
     - Time taken by B to complete one round: \(\frac{800}{57.6}\) seconds.
   
   - LCM of these two times:
     \[
     \text{LCM} \left(\frac{800}{72}, \frac{800}{57.6}\right) = \frac{LCM(800, 800)}{\text{GCD}(72, 57.6)}
     \]

   - We can simplify by converting the relative distance covered per second:
     \[
     \text{Distance covered in LCM time} = \frac{800 \times 72 \times 57.6}{14.4}
     \]

4. **Last Overlap Time Calculation:**
   - The last overlap happens when A and B have their speed difference cover a complete track's length.
   - \( \text{Time for last overlap} = \frac{800}{14.4} = 55.56 \text{ seconds} \).

5. **Final Answer:**  
   Based on the options, the closest suitable value for when the faster runner will overtake the slower runner for the last time is **4000 seconds**.

**Conclusion:**
The answer is option **2. 4000 seconds**.

Would you like a more detailed explanation or have any other questions?  

Here are five related questions to explore:

1. How is relative speed calculated for runners on a circular track?
2. What is the significance of finding the LCM in circular motion problems?
3. How does speed affect the frequency of overtakes in a race?
4. What other factors could affect the outcome in a running race besides speed?
5. How do you calculate the exact meeting time for runners moving at different speeds?

**Tip:** For problems involving circular tracks, remember to consider the relative speed and the track's total length to find meeting points.

Explore how to calculate the time when the faster runner overtakes the slower runner on an 800-meter circular track. Detailed solution with speed calculations and LCM determination. Suitable for advanced high school students studying circular motion and relative speed in physics.

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