Question

The ratio of the speed of a thief and a policeman is 2 : 3. The thief starts running from point A at the speed of 20 km\hr. After how much time will the police will catch the thief if he is 4200 m away from the thief? 

1. 8.6 min
2. 12.6 min
3. 25.2 min
4. 24.6 min

Answer 1

Correct Answer - Option 3 : 25.2 min

Given:

The ratio of thief and police = 2 : 3

Speed of thief = 20 km/hr

Distance between thief and police = 4200 m = 4.2 km

Formula used:

Speed = Distance/Time

Concept used:

If speed of body A is x m/s and speed of body B is y m/s then,

Relative speed of two bodies moving in same direction = (x – y) m/s

Relative speed of two bodies moving in opposite direction = (x + y) m/s

Calculations:

Let the speed of thief and police be 2x and 3x.

⇒ 2x = 20 km/hr

⇒ x = 10 km/hr

Speed of police = 3x

⇒ 3 × 10

⇒ 30 km/hr

Relative speed = 30 – 20

⇒ 10 km/hr

Time taken by police to catch the thief = 4.2/10 hr

⇒ 0.42 hr

⇒ 0.42 × 60

⇒ 25.2 min

∴ Police will catch the thief after 25.2 min.