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?

Thief’s speed  = 100 km/h,

Police speed initially = 75 km/h,

Police delay due to engine problem  = 30 minutes (or 0.5 hours),

Police speed after the problem is fixed = 120 km/h 

​$$\text{Time}= \frac{distance}{speed}$$​​

Distance by thief in 1 hour = 100 km

Distance by police in 1 hour = 75 km

total gap : 100 – 75 = 25 km

$$\star$$After engine problem thief went 50 km more in 30 min

Now total gap is: 25+50 = 75 km

new speed of police is 120 km/h

time taken to catch the thief is =$$\frac{75}{120-100}= \frac{75}{20}= 3.75 hr$$

Now total taken time is = 1hr + 0.5hr +  3.75 hr = 5.25 hr 

or 5 hours 15 minutes

​