Question

a thief runs from a police station at a uniform speed of 100m per.after 1 minute a policeman runs behind the thief to catch him.he goes at a speed of 10m/minute in the first minute and increases his speed by 10m
in each succeeding minute.after how many minutes will the policeman catch the thief

Answer 1

answer is 21 minutes because after 1 minute police runs behind the thief.
please see the picture

Answer 2

Step-by-step explanation:

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here....

theif's speed=100m./min

let time taken by police before catch the thief =x

then the time of theif being catched=x+1

as the police increase his speed=10m./min every minute

his time taken as AP-100,110,120....

Distance of the thief = $time ×speed \\</p><p> =100×(x+1)\\</p><p> =100x+100..........(1)$

Distance covered by police =sum of x terms of AP

=Sn=x/2(2×100+(x-1)10)

=Sn=x(100+5x-5)

=Sn=95x-5x^2...........(2)

as the distance covered by police and theif are same...

=equation 1=equation 2

= 95x-5x^2=100x+100

=5x^2-5x-100=0

= x^2-x-20=0

we solve the equation and get...

x=-4 and x=5

[as the time can't be negative]

= X=5

the time taken by police to catch the thief = 5 minutes