Question

A thief runs with the uniform speed of 50m/min. After 2 minutes a policemen runs after the thief to catch him. He goes 60 metres in first minute and increase his speed by 5m/min every succeeding minute. After how many min the policemen will catch the thief.

I got the answer as : the policeman will catch the thief when the thief will be at 350 metres and it will take 5 minutes .
I got the answer by writing in AP, i.e,
for thief ->100,150,200,250,300,350
for policeman->60,125,195,270,350.
I am not able to put it in the formula.

Answer 1

Solution-: According to sequence you are given
for thief ->100,150,200,250,300,350
for policeman->60,125,195,270,350. ,

Speed of the theif is 50 m/min

In 2 mins, the theif covers 100 m.

After 2 mins, the policeman runs to catch him, so in the third minute the policeman covers 60 m.

In the third minute the thief would cover 150 m.

Now policeman increases his speed by 5 m/ min

So, in the fourth minute:

Distance covered by policeman = 60 + 65 = 125 m

Distance covered by thief = 200 m

In the fifth minute:

Distance covered by policeman = 125 + 70 = 195 m

Distance covered by thief = 250 m

In the sixth minute:

Distance covered by policeman = 195 + 75 = 270 m

Distance covered by thief = 300 m

In the 7th minute:

Distance covered by policeman = 270 + 80 = 350

Distance covered by thief = 350 m

Hence, after 7 minutes the policeman will catch the thief.
So answer is 7 minutes.