A thief escaped from the police and drove away in a bike at 100 km/h. The police immediately started chasing at 75 km/h. After an hour, there was an engine problem in the police vehicle which took 30 minutes to set it right. Thereafter, the speed of the vehicle picked up to 120 km/h. After how much time was the thief caught?

Let say, from starting point thief is being caught at distance 'd' km.

So, Police covered (d-75) km at the speed of 120 km/h.

And, Thief covered (d-150) km at the speed of 100 km/h.

So, $$\frac{120}{100}=\frac{d-75}{d-150}.$$

or,$$120d-18000=100d-7500.$$

or,$$20d=18000-7500=10500.$$

or,$$d=525.$$

So, Police caught thief after speed up in = $$\frac{525-75}{120}\ hr\ =\frac{450}{120}\ hr=3.75\ hr.$$

So, Total time taken = (3.75+1.5) hr= 5.25 hr.

C is correct choice.