A thief escapes from a police station at 8:00 a.m. on a cycle at a speed of 50 km/h. A policeman starts chasing the thief on a motorbike at 9:30 a.m. at the speed of 65 km/h. At what distance from the police station will the policeman catch up with the thief?

325 km

Distance = Speed × Time

Distance cover by thief till 9:30 am = 50 × \(\frac{3 }{2 }\) = 75 km

Relative speed ( when moves in same direction ) = 65 - 50 = 15 km/h

Time taken = \(\frac{Distance  }{Speed }\) 

= \(\frac{75 }{15 }\)  = 5 hours

Distance cover by Policeman = 65 × 5 = 325 km