A passenger train departs from Delhi at 6 p.m. for Mumbai. At 9 p.m., an express train, whose average speed exceeds that of the passenger train by 15 km/hour leaves Mumbai for Delhi. Two trains met each other mid-route. At what time do they meet, given that the distance between the cities is 1080 km?

Option 4 : 6 a.m.

Let the average speed of passenger train = x km/hr;

Since average speed of express train is 15 km/hr more than that of a passenger train and

Both the trains are running in opposite directions;

∴ Average speed of express train = (x + 15) km/hr

Since two trains met each other mid-route, which means both trains covered 540 km;

∴ 540/x – 540/(x + 15) = 3

Solving the equation;

x = 45

∴ Average speed of passenger train = 45 km/hr

And Average speed of express train = 60 km/hr

Let the after t hours from 6 p.m., both the trains met;

∴ Distance travelled by passenger train in t hour = distance travelled by express train in

(t – 3) hour

⇒ 45 × t = 60 × (t – 3)

⇒ 15t = 180

⇒ t = 12 hours