Train A crosses a pole and platform in 18 secnds and 39 seconds respectively. The length of platform is 157.5 metre. What will be the lengt…

Solution
Let length of train A = $l$ metres
and speed of train A = $x$ m/s
Using, $time = \frac{distance}{speed}$
=> $\frac{l}{x} = 18$
=> $x = \frac{l}{18}$
Length of platform = $157.5$ metres
=> $\frac{157.5 + l}{x} = 39$
Substituting value of $x$, we get :
=> $\frac{157.5 + l}{39} = \frac{l}{18}$
=> $13l = 6l + 945$
=> $13l - 6l = 7l = 945$
=> $l = \frac{945}{7} = 135$ metres
$\therefore$ Length of train B
= $(\frac{135}{2}) + (157.5 \times 2)$
= $67.5 + 315 = 382.5$ metres