A thief is spotted by a policeman from a distance of 100 m. when the policeman starts the chase, the thief also starts running. If the speed of the thief be 8 km/hr and that of the policeman 10 km/hr, how far the thief will have run before he is overtaken?

400 m

From point A, Time taken by policeman to cover initial 100 m (Say Point B) (0.1km) = 1/100 hr = 36 sec

In 36 seconds  the thief has reached distance from B = 8/3600 * 36 = 0.08 km = 80 m

Now in 36 seconds the distance between them has reduced to 20 m, to reduce more 80 m more time taken = 4 times of 36 seconds

In next 144 seconds, policeman is at distance from point B = 10*144/3600 = 0.4 km

In next 144 seconds, thief is at distance from point B = 0.08+ 8*144/3600 = 0.08+0.32 = 0.4 km

Now they are at the same point, the thief has covered total distance from his original position = 400 m

The correct answer is Option (3) → 400 m