A policeman chases a thief. The speeds of the policeman and the thief are 8 km/h and 6 km/h, respectively. If the policeman started 10 minutes late, at what distance he will catch the thief?

Question

Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 24 Jul 2023 Shift 1)

Answer 1

Given:

Speed of thief = 6 km/h

Speed of policeman = 8 km/h

Formula Used:

Speed = Distance/Time

Concept Used:

If two objects are moving in the same direction with speeds S 1 and S 2 ,

Their relative speed is S 1 – S 2

Calculation:

Only the thief runs for 10 minutes.

Speed of thief in m/s = 6 km/h × 5/18 = 5/3 m/s

Time Taken in sec = 10 × 60 sec = 600 sec

Distance covered by the thief = Speed × Time

⇒ 5/3 m/s × 600 sec = 1000 m

Relative speed = 8 – 6 = 2 km/h

⇒ 2 × 5/18 m/s

⇒ 5/9 m/s

Time to catch the thief = Time required to cover 1000

⇒ 1000/5 × 9 s

⇒ 200 × 9 s

⇒ 1800 s = 30 min

Distance covered by the policeman in 30 min = 8 × 1/2

= 4 km.

∴ The policeman will catch the thief in 4 km.