A thief steals an item and escapes, running at 20 km/h. A policeman arrives at the spot of the crime after 6 minutes and immediately starts chasing the thief. 24 minutes after the policeman started to chase the thief, there is still a gap of 400 m between the two. At what distance from the spot of crime would the policeman catch up with the thief, and what is the speed at which the policeman ran?

Question

Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 26 Jul 2023 Shift 1)

Answer 1

Given:

Speed of thief = 20 km/h

Policeman delay = 6 minutes

Time after which the gap is 400 m = 24 minutes

Gap = 400 m

Formula Used:

Distance = Speed × Time

km/h to m/min = multiply with 1000/60

Calculation:

Distance covered by thief in 6 min = 20 × 1000/60 × 6 min = 2000 m

Total time thief has been running when the gap is 400 m

⇒ 6 + 24 = 30 min

Distance covered by thief in 30 min = 20 × 1000/60 × 30 min = 10000 m

Distance covered by a policeman in 24 minutes

⇒ 10000 m - 400 m = 9600 m

Speed of policeman = 9600 m / 24 min = 400 m/min

Speed of policeman in km/h = 400 m/min × 60 min/1000 = 24 km/h

Relative speed = 400 m/min - (20 × 1000/60) m/min

⇒ 400 - 1000/3 = 200/3 m/min

Time to close 400 m gap = 400 / (200/3) = 6 min

Total distance from the spot of crime when the policeman catches the thief

⇒ Distance = (1000/3) × (30 + 6) = 12000 m = 12 km

∴ Running at a speed of 24 km/h, the policeman will catch the thief at a distance of 12 km from the spot of the crime.