Two trains running at the rate of 75km and 60km an hour respectively on parallel rails in opposites directions, are observed to pass each other in 8 seconds and when they are running in the same direction at the same rates as before, a person sitting in the faster train observes that he passes the other in 33 seconds. Find the lengths of the trains.

Relative speed white running in opposite direction 12 

$= (75+60) kmph : =\left(135\times \frac{5}{18}\right) m{s}^{-1}=\frac{75}{2} m{s}^{-1}$

Again, relative speed while running in same direction 

$=(75-60) kmph=15 kmph =\left(15\times \frac{5}{18}\right) m{s}^{-1}=\frac{25}{6} m{s}^{-1}$

As we know, velocity =$\frac{Dis\tan ce }{ Time}$ 
$Dis\tan ce = Velocity\times Time$
Lengths of the both trains =$\left(\frac{75}{2}\times 8\right)=300$ meter

Now, as the faster train exceeds the slower train in the same direction in $33\frac{1}{2}$ seconds.

The length of the slower train = $\left(\frac{25}{6}\times 33.5\right)=131.25$ meter.

The length of the faster train =$300-131.25 = 168.75$ meter

(ans.) Faster train 168.75 meter & slower train 131.25 meter.