Correct Answer - Option 4 : 40 min
Given:
Length of road = 90 km
Speed of thief = 30 km/hr
Speed of policeman A = 70 km/hr
Speed of policeman B = 60 km/hr
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
Calculation:
When the policeman starts the chase, the thief has already covered 30 km
Relative speed of Policeman A with respect to thief = (70 – 30) km/hr
⇒ 40 km/hr
Time taken by the policeman A to catch the thief = 30/40 hr
⇒ 3/4 hr
⇒ (3 × 60)/4 min
⇒ 45 min
Relative speed of policeman B with respect to thief = 60 + 30
⇒ 90 km/hr
Time taken by the policeman B to catch the thief = 60/90 hr
⇒ 2/3 hr
⇒ (2 × 60)/3 hr
⇒ 40 min
∴ Policeman B will catch first in 40 min.