Train 'E' leaves at 9:00 PM on Wednesday from Kolkata station and reaches Bangalore station at 11:00 AM the next day, while train 'F' leaves at 8:30 PM on Wednesday from Bangalore station and reaches Kolkata station at 7:30 AM the next day. Find the time at which the two trains meet each other.

Solution

ATQ, Let the speed of the train 'E' and train 'F' be 'x' km/h, and 'y' km/h, respectively. For train 'E', from 9:00 PM to 11:00 AM next day: Total time = 14 hours Similarly, for train 'F' From 8:30 PM to 7:30 AM next day: Total time = 11 hours ATQ: Total distance between Kolkata and Bangalore = 14 X x = 11 X y Or, (x/y) = (11/14) Or, (x/y) = (11/14) Therefore, x = 11:14 Let the speed of train 'E' and train 'F' be '11a' km/h, and '14a' km/h, respectively. Distance travelled by train 'E' in 30 minutes = 11a X (30/60) = '5.5a' km Remaining distance between train 'E' and train 'F' when train 'F' started = 14 X 11a - '5.5a' = 148.5a km We know that, When two objects moving in opposite direction, then their relative speed = Sum of their individual speed Required time taken to meet = 148.5a / 25a = 5.94 hrs Time at which the trains will meet = 5.94 hours after train 'F' started = 2:24 AM next day