Question

A thief saw a policeman and he started running at a speed of 12 m/s. After a certain time, the policeman starts running behind the thief at a speed of 18 m/s. If the policeman covered a 540 m distance to catch the thief, the time (in seconds) after which the policeman started running is:

• A. 10
• B. 12
• C. 15
• D. 18

Answer 1

Answer:

C. 15

Let’s correct it carefully.

Given:

• Thief speed = 12 m/s

• Policeman speed = 18 m/s

• Distance covered by policeman till catch = 540 m

• Need: time thief got head start

  Time taken by policeman to cover 540 m

$t = \frac{540}{18} = 30 \text{ seconds}$

So policeman runs for 30 seconds.

Relative speed

$18 - 12 = 6 \text{ m/s}$

Distance thief gains in 30 seconds

$6 \times 30 = 180 \text{ m}$

Time thief had head start

$\text{Time} = \frac{180}{12} = 15 \text{ seconds}$