A thief steals an item and escapes, running at a speed of 15 km/h. A policeman arrives at the spot of the crime after 4 minutes and immediately starts chasing the thief. 16 minutes after the policeman started to chase the thief; there is still a gap of 200 m between the two. At what distance from the spot of the crime will the policeman catch up the thief and what is the speed (in km/h) of the policeman?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 6 km; 18.
Distance travelled by thief in 20 minutes = 15 × 20/60 = 5 km
As there is gap of 200m, distance = 5 - 0.2 = 4.8 km
Speed of policeman = 4.8/(16 ÷ 60)
⇒ 18 km/h
Relative speed = Speed of policeman - Speed of thief
⇒ 18 - 15 = 3 km/h
Time taken = Distance/Relative speed
⇒ (200 ÷ 1000)/3 = 1/15 hours
⇒ 1/15 × 60 = 4 minutes
Distance covered by thief in 4 minutes = 15 × 4/60 = 1 km
Total distance covered by thief = 5 + 1 = 6 km
Hence the required answer is 6 km; 18.