Train A crosses train B completely in 90 seconds, with the trains running in opposite directions. The lengths of the trains A and B are 900 metres and 1800 metres. respectively. If the speed of train A is 45 km/h, then in how much time can train B cross a stationary pole?

$\frac{720}{7}$ seconds

Let speed of train B = S km/h

Relative speed ( when both moves in same direction )  = ( S + 45 ) km/h

Distance = ( 900 + 1800 ) = 2700 m

We know ,

Speed = \(\frac{Distnace}{Time}\)

= \(\frac{2700}{90}\) = 30 m/sec

30 m/sec = 30 × \(\frac{18}{5}\) km/h = 108 km/h

 ( S + 45 ) km/h= 108 km/h

S = 63 km/h = \(\frac{35}{2}\) m/sec

Time taken by train B to cross pole = \(\frac{1800×2 }{35}\)

= \(\frac{720 }{7}\) sec