Question

A thief ran away from the police station at a uniform speed of 100m/min after one minute a police man run behind the thief he goes at a speed of 100m/min in first min and increasing the speed 10m/min on each succeeding minute after how many min the police catch thief?

Answer 1

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