A thief steals an item and escapes, running at 20 km/h. A policeman arrives at the spot of the crime after 6 minutes and immediately starts chasing the thief. 24 minutes after the policeman started to chase the thief, there is still a gap of 400 m between the two. At what distance from the spot of crime would the policeman catch up with the thief, and what is the speed at which the policeman ran?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 12 km; 24 km/h.
Given that, speed of thief = 20 km/h
Delay by police = 6 min
Distance = Speed × Time
Distance covered by thief in 6 min = (20 × ) × (6 × 60)
⇒ 100 × 20 = 2000 m
When the gap is 400 m, total time thief has been running = 24 + 6 = 30 min
Distance covered by thief in 30 min = (20 × ) × (30 × 60)
⇒ 100 × 100 = 10000 m
Distance covered by policeman in 24 min = 10000 - 400 = 9600 m
Speed of policeman = = 400 m/min
Speed of policeman in km/h = × 60 = 24 km/h
Now, relative speed of thief and policeman = 24 - 20 = 4 km/h
Relative speed in m/min = = m/min
Time taken to cover the gap of 400 m = = 6 min
Total time taken by the policeman to catch the thief = 30 + 6 = 36 min
Total distance covered = 20 ×
⇒ 2 × 6 = 12 km
Hence the required distance is 12 km and required speed is 24 km/h.