Two trains one of length $100\text{m}$ and another of length $125\text{m}$, are moving in mutually opposite directions along parallel lines, meet each other, each with speed $10\text{m/s}$. If their accelerations are $0.3{\text{m/s}}^2$ and $0.2{\text{m/s}}^2$ respectively, then the time they take to pass each other will be

The correct option is B $10\text{s}$
Relative velocity of one train w.r.t. other
$u=10+10=20\text{m/s}.$

Relative acceleration $a=0.3+0.2=0.5{\text{m/s}}^2$

If trains cross each other, then from $s=ut+\frac{1}{2}a{t}^2$
as, $s=s_1+s_2=100+125=225\text{m}$

$\Rightarrow 225=20t+\frac{1}{2}\times 0.5\times t^2\Rightarrow 0.5t^2+40t-450=0$

$\Rightarrow t=\frac{-40\pm \sqrt{1600+4\times \left(0.5\right)\times 450}}{1}=-40\pm 50$

$\therefore t=10\text{sec}$ (Taking +ve value).

Hence, option $\left(\text{B}\right)$ is the right choice.