Two identical trains A and B running in opposite directions at the same speed take 2 min to cross each other completely. The number of bogies of A increased from 12 to 16. How much more time would they now require to cross each other?
Two identical trains A and B running in opposite directions at the same speed take 2 min to cross each other completely. The number of bogies of A increased from 12 to 16. How much more time would they now require to cross each other?
1). 40 second
2). 72 second
3). 60 second
4). 20 second
1 answers
Let the length of each bogie be L, and their velocities be v each.
Initial length of each train = 12L.
Whenever a train crosses another train, each train travels a distance equal to the sum of their lengths at relative speed.
∴ in this case, distance traveled = 12L + 12L = 24L
Since the trains are running in the opposite directions, we have
Relative speed = v + v = 2v
Time taken to cross each other = 24L/2v = 12L/v
⇒ 120 = 12L/v
⇒ L/v = 10
Now, given that the length of train A increased by 4 bogies ⇒ New Length of A = 16L
∴ New distance to be traveled = 16L + 12L = 28L
Hence, time taken now to cross each other = (16L + 12L)/2v = 14L/v = 140 sec
Hence, the time would increase by 20 sec.