Multiple choice

A train travelling at 72 km/hr crosses an another train having half its length and travelling in opposite direction at 63 km/hr in 15 seconds. Faster train also passed a railway platform in 50 second. find length of smaller train is what percent of length of platform?

  1. 34%

  2. 35%

  3. 36%

  4. 30%

  5. 32%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let L1 be the length of the faster train and L2 be the length of the smaller train. L2 = 0.5 * L1. Relative speed = 72+63 = 135 km/hr = 37.5 m/s. Total distance = (L1 + 0.5*L1) = 1.5*L1 = 37.5 * 15 = 562.5. So L1 = 375, L2 = 187.5. Faster train passes platform in 50s: (375 + P) = 20 * 50 = 1000, so P = 625. Ratio L2/P = 187.5/625 = 0.30 or 30%.

AI explanation

Let the length of the faster train be L, making the length of the slower train L/2. Their relative speed in opposite directions is 72 + 63 = 135 km/h, which converts to 135 multiplied by 5/18, equaling 37.5 m/s. The total distance covered in 15 seconds is 37.5 multiplied by 15, giving 562.5 meters. Setting the sum of their lengths to this distance gives L + L/2 = 562.5, meaning 1.5L = 562.5, so L = 375 meters. The length of the smaller train is half of this, which is 187.5 meters. The faster train crosses the platform in 50 seconds at 72 km/h, which is 20 m/s. The platform length is (20 multiplied by 50) minus 375, equaling 625 meters. The required percentage is (187.5 / 625) multiplied by 100, which equals 30%.

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