Question

A thief runs with a uniform speed of 100m/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

thief speed=100m/min
time taken by police before catching the thief= x
then the time of thief being catched= x+1
as the police increases his speed 10 m/min every succeeding minute,
his time taken forms an ap- 100,110,120......

distance of thief=time*speed
=100*(x+1)-----------------1

distance covered by police=sum of x terms of the ap
sn=x/2 (2(100) + (x-1) 10)
sn=x(100+5x-5)
sn=95x-5x square ---------------2
 as the distance covered by police and thief are same,
1=2
95x-5x square=100*(x+1)
95x-5x square=100x + 100
5x square-5x-100=0
x square-x-20=0

if we solve this equation,
we will get x= -4 and x=5
as time cannot be negative, 5 is the right answer.
thus the time taken by the police to catch the thief=5 mins.


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Answer 2

Answer:

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