Question

A thief runs ???? with a uniform speed of 100m/min. After 1min a policeman ???? ???? runs after the thief to catch him. He goes with a speed of 100m/min in the first min and increases his speed by 10m/min every succeeding min. After how many min the ???? policeman will catch the thief .

Answer 1

Let after time t the police will catch the thief.

Distance travelled by Thief in time t

= 100m/min × t min = 100t m

Also, the thief started 1 min earlier

so, net distance covered by thing in t+1 min

= 100t + 100 m


Distance travelled by police in t min

= 100 + {100+10} +{100+10×2} + .....+ 100+{10×(t-1)}

= 100 + {100 + 100 + (t -1 - 1)10}

{as Sn= 2a+(n-1)d}

= 100 + { 200 + 20t - 20 }

= 100 + 200 + 20t - 20

= 280 + 20t


When the police will catch the thief

100t + 100 = 280 + 20t

or, 100t - 20t = 280 - 100

or, 80t = 180

or, t = 18/8 = 9/4 = 2.25 min



So, the police will catch the thief after

2.25 minutes.