# Problems on Trains - Aptitude Questions and Answers - RejinpaulPlacement

43.
A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train? [S.B.I.P.O. 1999]

Solution:   Relative speed = (120 + 80) km /hr = 200 km/hr
= [200 * (5/18)] m/sec
= (500/9) m/sec.

Let the length of the other train be x metres.

Then, (x + 270) / 9 = (500/9)
=> x + 270 = 500
=> x= 230
44.
Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is: [S.S.C 2003]

Solution:   Let the speed of each train be x m/sec.

Then, relative speed of the two trains = 2x m/sec

So, 2x = (120 + 120) / 12
=> 2x = 20
=> x = 10

Speed of each train = 10 m/sec
= [10 * (18/5)] km/hr
= 36 km/hr.
45.
Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time(in seconds will they cross each other travelling in opposite direction? [S.S.C 2004]

Solution:   Speed of the first train = (120/10) m/sec = 12 m/sec.

Speed of the second train = (120/15) m/sec = 8 m/sec.

Relative speed = (12 + 8) m/sec = 20 m/sec

Required time = (120 + 120) / 20 sec = 12 sec.
46.
A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the train is :

Solution:   Let the speed of the second train be x km/hr.

Relative speed = (x + 50) km/hr
= [(x + 50) * (5/18)] m/sec
=[(250 + 5x) / 18] m/sec.

Distance covered = (108 + 112) = 220 m.

220 / [(250 + 5x)/18] = 6
=> 250 + 5x = 660
=> x = 82 km/hr
47.
A train X speeding with 120 kmph crosses another train Y, running in the same direction, in 2 minutes. If the length of the trains X and Y be 100 m and 200 m respectively, what is the speed of train Y?

Solution:   Let the speed of the train Y be x km/hr.

Speed of X relative to Y = (120 - x) km/hr
= [(120 – x) * (5/18)] m/sec
= [(600 -5x) / 18] m/sec.

300 / [(600 – 5x) / 18] = 120
=> 5400 = 120(600 – 5x)
=> x = 111 km/hr.
48.
Two trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 8 seconds. The length of the faster train is:

Solution:   Relative Speed = (36 + 45) km/hr = 81 km/hr
[81 * (5/18)] m/sec
= (45/2) m/sec

Length of train = [(45/2) * 8] m = 180 m.
49.
Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train? [R.R.B 2001]