Multiple choice

Two trains while moving in opposite direction on parallel tracks, take 10 seconds to cross each other. However, if they travel in the same direction, the longer train, which is faster than the shorter train, crosses the shorter train in 30 seconds. If the length of the longer train is decreased by 75%, it takes 12 seconds less to cross the shorter train traveling in the same direction. Find the time taken by the longer train to cross a tunnel twice its length, if the difference between the lengths of the trains is 50 m?

  1. 28 seconds

  2. 20 seconds

  3. 24 seconds

  4. 32 seconds

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let longer train length = L, shorter = S, speeds = Vl, Vs. Opposite direction: (L+S)/(Vl+Vs) = 10. Same direction: (L+S)/(Vl-Vs) = 30. Reduced length: (0.25L+S)/(Vl-Vs) = 18. Also L - S = 50. From first two equations: 10(Vl+Vs) = 30(Vl-Vs), so Vl = 2Vs. Using this and the equations, we find Vs = 25, Vl = 50, L = 400. Tunnel length = 2L = 800, crossing time = (L+2L)/Vl = 3L/Vl = 1200/50 = 24 seconds.

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