Multiple choice

The ratio of lengths of two trains P and Q is 3 : 5. Both the trains start running from the same station in the same direction but at different time interval. The time taken by train P to cross a tunnel whose length is 50% more than the sum of the lengths of the two trains is 46 minutes less than that by train Q. Find the length of tunnel. Speed of train P and Q is 72 km/hr and 54 km/hr respectively.

  1. 806

  2. 82.4

  3. 86.4

  4. 88.6
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let lengths be 3x and 5x. Tunnel length = 1.5 * (3x + 5x) = 12x. Speed P = 20 m/s, Speed Q = 15 m/s. Time P = (3x + 12x) / 20 = 15x / 20 = 0.75x. Time Q = (5x + 12x) / 15 = 17x / 15. Difference = 17x/15 - 0.75x = 46 minutes = 2760 seconds. (17x - 11.25x) / 15 = 2760 => 5.75x = 41400 => x = 7200. Tunnel = 12 * 7200 = 86400 meters = 86.4 km.

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