Question

A thief ran from the police custody at
a speed of 9km/hr. After 30minutes,
police got alerted and started chasing
him at the speed of 36km/hr. After
how much time since he ran, the thief
could be nabbed?
(A) 40 minutes
(B) 45 minutes
(C) 50 minutes
(D)60 minutes
​

Answer 1

Answer:

Explanation:

45 min

Answer 2

Given:

A thief ran from the police custody at

a speed of 9km/hr. After 30minutes,

police got alerted and started chasing

him at the speed of 36km/hr.

To find:

Time after which the thief can be caught?

Calculation:

First of all, let's calculate the initial distance between the thief and the police when the police got allerted:

$\sf \therefore \: d = 9 \: km {hr}^{ - 1} \times 30 \: min$

$\sf = > \: d = 9 \: km {hr}^{ - 1} \times \dfrac{1}{2} \: hr$

$\sf = > \: d = 4.5 \: km$

Now , let time taken to catch the thief be "t":

• So , in this time "t" , the final position of the thief and the police will be safe.

$\sf \therefore \: d_{police} = d_{thief} + 4.5$

$\sf = > \: (36 \times t) = (9 \times t) + 4.5$

$\sf = > \: 36t = 9t + 4.5$

$\sf = > \: 27t = 4.5$

$\sf = > \: t = 0.16 \: hr$

$\sf = > \: t = 0.16 \times 60 \: min$

$\sf = > \: t = 10 \: min$

So total time after which thief can be caught will be ( 30 + 10 ) = 40 seconds.

$\boxed{ \bold{option \: A)}}$