Question 10

# Three friends Pradeep, Suresh and Subodh workin the same office. During an extended weekend theydecided to go together on a family trip to Corbett National Park. They started from office in their owncar but at different time and travelled in the same direction at speeds of 50 km/hr, 60 km/hr and 75km/hr respectively. Suresh and Subodh overtook Pradeep at the same point. If Suresh started 90minutes after Pradeep, how many minutes after Pradeep did Subodh start from the office?

Solution

Consider the instance when Suresh just starts from the office.
Distance that Pradeep has already covered in that time = 50*1.5 = 75 km

Now, by concept of relative velocity, time taken by Suresh to just overtake Pradeep = 75/(60-50) = 7.5 hours
Hence, the point of overtaking on the route is = 60*7.5 = 450 km from the office

Subodh also overtakes Pradeep at the same point. Pradeep covers this 450 km distance in 9 hours.
Subodh can cover this 450 km in 6 hours.
Hence, Subodh can leave 9 - 6 = 3 hours after Pradeep does.