Q 11-02-085JEE MainJEE Main 2023 (13 Apr, Shift 1)Medium
Two trains $A$ and $B$ of length $l$ and $4l$ are travelling into a tunnel of length $L$ in parallel tracks from opposite directions with velocities $108\ \text{km h}^{-1}$ and $72\ \text{km h}^{-1}$, respectively. If train $A$ takes $35$ s less time than train $B$ to cross the tunnel then, length $L$ of tunnel is (Given $L=60l$)
Answer: (C) $1800\ \text{m}$
To cross the tunnel a train covers $L+$ its own length. $v_A=30\ \text{m s}^{-1}$, $v_B=20\ \text{m s}^{-1}$:
$$\frac{64l}{20}-\frac{61l}{30}=35\ \Rightarrow\ 3.2l-2.033l=35\ \Rightarrow\ l=30\ \text{m}$$
$L=60l=1800\ \text{m}$.
Solution by Sreeraj P, M.Sc Physics