The speed of a thief is times the speed of a policeman. The thief covers a distance of 6 km before he was caught by the policeman in 30 minutes. Initially, what was the distance between the policeman and the thief in km?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 1.5.
Given that, speed of thief = of speed of policeman
Ratio of speeds of thief and policeman = 4 : 5
Time of travel of thief and policeman is same, i.e, 30 minutes
Ratio of distance covered by thief and policenman = 4 : 5
Let the total distance covered by policeman be x km.
Distance covered by thief after policeman started chasing him = 6 km
Initial distance between them = (x - 6) km
Now, let the distance covered by both the thief and the policeman be 4a and 5a km.
Given that, 4a = 6km
⇒ a = 6/4
⇒ 5a = (3/2) × 5 = 7.5
Total distance covered by policeman, x = 5a = 7.5 km
Initial distance between them = (x - 6) km
⇒ 7.5 - 6 = 1.5 km