Problem Solving

A tractor towing 120 trolleys overtakes Sharan who is going in the same direction driving his CAR in 36 seconds. It travels for half an hour from the time it starts overtaking Sharan to before it finishes crossing Deepak (riding his bike) coming from the opposite direction in 24 seconds. In how much time (in minutes) after the tractor has crossed Deepak, does Sharan meet Deepak? (the lengths of CAR and bike are negligible)
(1) 59 minutes 18 seconds
(2) 60 minutes
(3) 59 minutes
(4) 59 minutes 36 seconds





My Take on this:

I am assuming the speeds of Deepak and Sharan to be equal.
Let the speed of the tractor be u
Let the speed of Deepak = Sharan = v
Let the length of the train be 120

We have: u - v = 120*60/36 = 200
Also, u + v = 120*60/24 = 300

=> u = 250 and v = 50

Tractor traveled after overtaking Sharan for = 30 - 3/5 + 2/5 = 149/5 minutes

Distance traveled by tractor = (149/5)* 250 = 7450
Distance traveled by Sharan = 1490

=> Distance between Sharan and Deepak = 7450 - 1490 = 5960

Deepak and Sharan will meet after = Distance between them / 2v

=> Time = 5960/(2*50) = 59.6 minutes = 59 minutes and 36 seconds


Am i correct??? Or did i commit a mistake somewhere in between??