We are given that a thief is initially 800 meters ahead of a policeman. The thief runs at a speed of 20 km/h, while the policeman runs at a speed of 25 km/h. We need to find the distance between them after 9 minutes.

Let's solve this step-by-step:

1. First, convert their speeds from km/h to m/min. Knowing that 1 km = 1000 meters and 1 hour = 60 minutes, we have:
   • Speed of Thief: \frac{20 \, \text{km/h} \times 1000}{60} = \frac{20000}{60} = 333.33 \, \text{m/min}
   • Speed of Policeman: \frac{25 \, \text{km/h} \times 1000}{60} = \frac{25000}{60} = 416.67 \, \text{m/min}
2. Calculate the gain in distance by the policeman every minute, which is the relative speed:
   • Relative Speed = Speed of Policeman - Speed of Thief = 416.67 - 333.33 = 83.34 \, \text{m/min}
3. After 9 minutes, the distance covered by this relative speed would be:
   • Distance Gained in 9 Minutes = 83.34 \, \text{m/min} \times 9 \, \text{min} = 750.06 \, \text{m}
4. Since the initial distance between them is 800 meters, the final distance will be:
   • Distance Between Them After 9 Minutes = Initial Distance - Distance Gained = 800 - 750.06 \approx 50 \, \text{meters}

Thus, the distance between the thief and the policeman after 9 minutes is approximately 50 meters.

Correct Answer: 50 metres