Two trains each $50\text{m}$ long are moving parallel towards each other at speeds $10\text{m/s}$ and $15\text{m/s}$ respectively. Time taken by them to pass each other is

The correct option is B $4\text{s}$
Velocity of train $1=15\text{m/s}$
Velocity of train $2=-10\text{m/s}$
$(\because$ Train $2$ is moving in opposite direction to that of train $1)$

Let $V_r$ be the relative velocity of the train $1$ w.r.t. train $2$
$\Rightarrow V_r=15-(-10)=25\text{m/s}$

Distance travelled by both trains to cross each other is given by
$d=50\text{m}+50\text{m}$
$d=100\text{m}$

$\therefore$ Time after which they will pass each other $=\frac{d}{V_r}=\frac{100}{25}=4\text{s}$