Two trains ' A ' and ' B ' of length ' \(l\) ' and ' \(4 l\) ' are travelling into a tunnel of length ' \(L\) ' in parallel tracks from opposite directions with velocities \(108 \mathrm{~km} / \mathrm{h}\) and \(72 \mathrm{~km} / \mathrm{h}\), respectively. If train 'A' takes 35s less time than train 'B' to cross the tunnel then, length 'L' of tunnel is : (Given \(\mathrm{L}=60 \mathrm{l}\) )

JEE Main · 2023 · 13 Apr 2023 · Shift 1 · Kinematics

Two trains ' A ' and ' B ' of length '

l

' and '

4 l

' are travelling into a tunnel of length '

L

' in parallel tracks from opposite directions with velocities

108 km / h

and

72 km / h

, respectively. If train 'A' takes 35s less time than train 'B' to cross the tunnel then, length 'L' of tunnel is :
(Given

L = 60 l

)

Answer: (C)

Convert velocities:

v_{A} = 108 km/h = 30 m/s

v_{B} = 72 km/h = 20 m/s

.

For a train to completely cross a tunnel, it travels a distance equal to (tunnel length + train length).

Time for train A:

t_{A} = \frac{L + l}{30}

Time for train B:

t_{B} = \frac{L + 4 l}{20}

Given

t_{B} - t_{A} = 35

s and

L = 60 l

\frac{60 l + 4 l}{20} - \frac{60 l + l}{30} = 35

\frac{64 l}{20} - \frac{61 l}{30} = 35

\frac{96 l - 61 l}{30} = 35

\frac{35 l}{30} = 35

l = 30

m

Therefore,

L = 60 l = 60 \times 30 = 1800

JEE Main · 2023 · 13 Apr 2023 · Shift 1 · Single correct option