Question

A thief saw a policeman, and he started running at a speed of 18 m/s. After 12 seconds, the policeman starts running behind the thief at a certain speed. If the policeman covered 864 meters distance to reach the thief, then the speed (in m/s) of the policeman is:

• A. 28
• B. 15
• C. 30
• D. 24

Answer 1

Answer:

D. 24

The 864 m is the distance the policeman runs to catch up, not the thief’s total distance.

Head start of thief

Thief runs for 12 seconds at 18 m/s:
$\text{Head start} = 18 \times 12 = 216 \text{ m}$

Let policeman’s speed = (v) m/s

Time taken by policeman to catch thief:
$t = \frac{864}{v}$

In this time, thief also moves further

Distance covered by thief during this time:
$18 \times \frac{864}{v}$

Catching condition

Total distance thief covers = distance policeman covers:
$216 + 18 \times \frac{864}{v} = 864$

Solve

$216 + \frac{15552}{v} = 864$
$\frac{15552}{v} = 648$

$v = \frac{15552}{648} = 24$

Final Answer: 24 m/s