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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 km/h and 72km/h, respectively. If train ‘A’ takes 35s less time than train ‘B’ to cross the tunnel then, length ‘L’ of tunnel is (Given L = 60l)

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a

2700m

b

1800m

c

1200m

d

900m

answer is A.

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Detailed Solution

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$T_{B} - T_{A} = 35 \Rightarrow \frac{4 l + L}{20} - \frac{l + L}{30} = 35$
$[\frac{64}{20} - \frac{61}{30}] \times l = 35 \Rightarrow \frac{3 \times 64 - 2 \times 61}{60} × l = 35$
$\frac{192 - 122}{60} \times l = 35 \Rightarrow l = 6 \times 5 = 30$

$L = 60 \times 30 = 1800 m$

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