A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km/h and 11 km/h, respectively. What is the distance (in metres) between them after 9 minutes?

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Accepted Answer

Step 1: Convert speeds from km/h to m/min.
- Thief's speed = 10 km/h = (10 × 1000) / 60 = 166.67 m/min
- Policeman's speed = 11 km/h = (11 × 1000) / 60 = 183.33 m/min

Step 2: Calculate relative speed of policeman with respect to thief.
- Relative speed = 183.33 - 166.67 = 16.66 m/min

Step 3: Calculate distance covered by policeman relative to thief in 9 minutes.
- Distance covered = relative speed × time = 16.66 × 9 = 150 m

Step 4: Initial distance between them = 200 m.
- Distance between them after 9 minutes = 200 - 150 = 50 m

Step 5: Check options. The closest correct answer is 50 m.

Rechecking calculations:
- Speeds in m/min: 10 km/h = 10000 m / 60 min = 166.67 m/min
- 11 km/h = 11000 m / 60 min = 183.33 m/min
- Relative speed = 16.66 m/min
- Distance covered in 9 min = 16.66 × 9 = 149.94 ≈ 150 m
- Remaining distance = 200 - 150 = 50 m

Therefore, the correct answer is 50 m.

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