A thief pursued by a policeman was 150 m ahead at the start. If the ratio of the speed of the policeman to that of the thief was 5 : 4, then how far (distance in metres) could the thief go before he is caught by the policeman?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 600.
Given that, distance between thief and policeman = 150 m
Ratio of speeds of policeman and thief = 5 : 4
When policeman is chasing a thief, they both move in same direction, then their relative speed is equal to the difference between their individual speeds.
Distance = Speed × Time
Let the speed of the policeman and the thief be 5x m/sec and 4x m/sec respectively.
Relative speed = Difference between the individual speeds
⇒ 5x - 4x = x m/sec
Time taken by the policeman to chase the thief = sec
So, distance covered by thief in sec = × 4x
⇒ 150 × 4 = 600 m
Hence the distance (in meters) covered by the thief before he was caught is 600.