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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)

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best_answer

Given, Speeds: A = 30 m/s, B = 20 m/s

Lengths: A=l, B=4 l

Tunnel length: L=60 l

As we know, A takes 35 s less than B.

\begin{aligned} &t_A=\frac{L+l}{30}, \quad t_B=\frac{L+4 l}{20}\\ &t_B-t_A=35\\ &\frac{L+4 l}{20}-\frac{L+l}{30}=35 \end{aligned}

\begin{gathered} \frac{(3(L+4 l)-2(L+l))}{60}=35 \\ \frac{L+10 l}{60}=35 \\ L+10 l=2100 \end{gathered}

As, L=60 l,

\begin{aligned} &60 l+10 l=2100 \quad \Rightarrow \quad 70 l=2100 \quad \Rightarrow \quad l=30 m\\ &L=60 \times 30=1800 m \end{aligned}

Posted by

Divya Sharma

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