Question

A thief runs with a uniform speed of 10m/minute . After one minute a policeman runs after the thief to catch him. He goes with a speed of 100m/minute in the first minute and increases his speed by 10m/min every succeeding minute. After how many minutes the police man will catch the thief ?

Answer 1

Heya Mate !!!

Here's Your Answer ⏬

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Step by Step Explanation ;-
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=> Let the police catch the thief in n min

=> As the thief ran 1 min before the police...time taken by the thief before being caught = (n+1) min

=> Distance travelled by the thief in (n+1) min = 100(n+1)m

=> Speed of police in 1st min=100m/min

=> Speed of police in 2nd min=110m/min

...3rd min = 120m/min.........so on

100,110,120,............ this forms an AP


=> Total distance travelled by the police in n min = n/2(2 x 100 +(n-1)10)

On catching the thief by police,distance traveled by thief= distance travelled by the police.

=> 100(n+1)= n/2(2 x 100 + (n-1)10)

=> 100n + 100= 100n +n/2(n-1)10

=> 100=n(n-1)5

=> n2 -n-20 = 0

=> (n-5)(n+4) = 0

=> n-5 = 0

=> n= 5    OR       n= -4...(but this is not possible)

=> So, n= 5

• Time taken by the policeman to catch the thief = 5min.

Answer 2

Answer:

Complete step by step answer:

• Policeman runs with speed = 10 m/min. Let us consider the policeman who catches the thief in 'n' minutes. The policeman starts running after the thief began to run and finished running 1 min. Therefore, the time taken by the thief until he gets caught is 'n+1' minute.