Question

A thief runs with a uniform speed of 100 m/minute. After one minute, a policeman runs after the

thief to catch him. He goes with a speed of 100 m/minute in the first minute and increases his

speed by 10 m/minute every succeeding minute. After how many minutes the policeman will

catch the thief. What value is depicted in this question?

Answer 1

5 minutes is the correct answer

Answer 2

let time taken by theif= n minutes
distance covered by thief = speed * time= 100n
policeman speed = 100,110,120_ _ _ (n-1)terms
so, by applying sum formula
100n = n-1/2(2a+(n-1)d)
200n=n-1(200+10n-20)
200n=180n+10n2(square)-180-10n
0=10n2(square)-30n-180
0=n2(square)-3n-18
now by middle term splitting,
0=n2(square)-6n+3n-18
0=n(n-6)+3(n-6)
n=6 or n=-3
n= -3 not possible
hence n=6
therefore Policeman will Catch thief in n-1 time that is 6-1 = 5 minutes