Question

A thief runs away from a police station with a uniform speed of 100 m/minute. After one minute, a policeman runs behind the thief to catch him. He goes at a speed of 100 m/minute in first minute and increases his speed by 10 m/min in each succeeding minute. How many minutes will the policeman take to catch the thief?

Answer 1

Answer:

he will catch thief after 12 min

Answer 2

5 minutes

Step-by-step explanation:

Let's say that the police caught the thief after n minutes of his start time.

Distance traveled by police every one minute duration from beginning = 100 + 110 + 120 + 130... +[ 100+(n-1)10 ]

 

We have expressed the distance as an arithmetic progression.

When the thief is caught by police, the distance traveled by the police and thief are equal.

 So we get (n/2)[ 200+ (n-1)10 ] = (n+1)×100

 

Solving the above expression, we get (n-5)(n+4) = 0

n can be +5 or -4. Since time cannot be negative. We get n = +5.

So the police caught the thief 5 minutes after the police started chasing or 6 minutes after the thief started running.