Multiple choice

Two trains I and II are running at speeds of 72 km/hr and 90 km/hr, respectively, on parallel tracks. When running in opposite directions, they pass each other in 10 seconds. When running in the same direction, a person sitting in the faster train (II) finds that he passes the other train (I) in 30 seconds. Find the lengths of the trains.

  1. Train I - 150 m, Train II - 300 m

  2. Train I - 250 m, Train II - 200 m

  3. Train I - 100 m, Train II - 350 m

  4. Train I - 150 m, Train II - 150 m

  5. None of these
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A Correct answer
Explanation

Let L1 and L2 be the lengths of the trains. The relative speed in opposite directions is 72+90 = 162 km/hr = 45 m/s, so L1+L2 = 45 * 10 = 450 m. In the same direction, the relative speed is 90-72 = 18 km/hr = 5 m/s, so L1 = 5 * 30 = 150 m. Thus, L2 = 450 - 150 = 300 m.

AI explanation

Using the relative speed formula for opposite directions, the sum of their lengths is (72 + 90) * (5/18) * 10 = 450 meters. Using the relative speed formula for the same direction, the length of train I is (90 - 72) * (5/18) * 30 = 150 meters, because the relative speed of the faster train applies to the length of the slower train. Subtracting this from the total length gives the length of train II as 450 - 150 = 300 meters, so the result is Train I - 150 m, Train II - 300 m.

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