A thief was spotted by a policeman at a distance of 1200 m and he started chasing him. The thief ran 6.4 km in 52 minutes and the policeman also ran the same distance in 40 minutes. Find the distance the thief had run before he was caught.

Here, thief ran 6.4 km in 52 minutes i.e. (52/60) hours (As 1 hour = 60 minutes) Speed of the thief = Distance/Time 6.4/ (52/60) = 6.4 x 60/52 = 96/13 km/h Now, a policeman ran 6.4 km in 40 minutes = 40/60 hours Speed of the policeman Distance/ Time =6.4 x 60/40 = 48/5 km/h As a policeman chases a thief.   Hence, they run in the same direction Relative speed when running in the same direction =48/5-96/13=144/65 Now, the time taken by a policeman to cover 1200m, 1200/1000 = 1.2km distance Now, the required distance for a thief, Speed x Time = 96/13 x 13/24 =96/24= 4 km Hence, the thief had to run 4 km before he was caught.