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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

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 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)
 

Option: 1

2700 m


Option: 2

1800 m


Option: 3

1200 m

 


Option: 4

900 m


Answers (1)

best_answer

\begin{aligned} &\begin{aligned} & \mathrm{V}_{\mathrm{A}}=108 \times \frac{5}{18}=30 \mathrm{~m} / \mathrm{s} \\ & \mathrm{V}_{\mathrm{B}}=72 \times \frac{5}{18}=20 \mathrm{~m} / \mathrm{s} \end{aligned}\\ &\begin{aligned} \mathrm{T}_{\mathrm{A}} & =\frac{\ell+\mathrm{L}}{30}, \mathrm{~T}_{\mathrm{B}}=\frac{4 \ell+\mathrm{L}}{20} \\ \mathrm{~T}_{\mathrm{A}} & =\mathrm{T}_{\mathrm{B}}-35 \end{aligned} \end{aligned}

\begin{aligned} & \frac{\ell+\mathrm{L}}{30}=\frac{4 \ell+\mathrm{L}}{20}-35 \\ & \text { Given, } \mathrm{L}=60 \ell \\ & \frac{61 \ell}{30}=\frac{64 \ell}{20}-35 \\ & \frac{192 \ell-122 \ell}{60}=35 \\ & 70 \ell=60 \times 35 \\ & \ell=30 \mathrm{~m} \\ & \mathrm{~L}=60 \ell=1800 \mathrm{~m} \end{aligned}

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Ritika Kankaria

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