A train $108$ m long moving at a speed of $50$ km/hr crosses a train $112$ m long coming from the opposite direction in $6$ seconds. What is the speed of the second train ?

The correct option is A $82$ km/hr
Let the speed of the second train be $x$ km/hr
Relative speed of train $=(x+50)$ km/hr $=(x+50)\times \frac{5}{18}$ m/s
Total time taken $=$ $=\frac{\text{Sum of lengths of both the trains}}{\text{Relative speed}}$
$=\frac{108m+112m}{(x+50)\times 5/18}$
$\Rightarrow \frac{220\times 18}{(x+50)\times 5}=6$

$\Rightarrow 44\times 3=x+50$

$\Rightarrow 132=x+50$

$\Rightarrow x=132-50=82$ km/hr