Two trains A and B of length l and 4l are travelling into a tunnel...

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 $108km{h}^{- 1}$ and $72km{h}^{- 1},$ respectively. If train $A$ take $35s$ less time than train $B$ to cross the tunnel then, length $L$ of tunnel is:

(Given $L = 60l$ )

Options

A $1200m$
B $900m$
C $1800m$
D $2700m$

Correct answer

C. $1800m$

Step-by-step solution

The time taken for $A$
$\Delta{t}_{A} = \dfrac{l + L}{{V}_{A}}$
The time taken for $B$
$\Delta{t}_{B} = \dfrac{4l + L}{{V}_{B}}$
It is given that $B$ takes more time than $A$ . So,
$⇒ \dfrac{4l + L}{20} - \dfrac{l + L}{30} = 35$
$⇒ \dfrac{64l}{20} - \dfrac{61l}{30} = 35$
$⇒ l = \dfrac{35 \times 600}{700} = 30m$
Therefore,
$L = 1800m$ .

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