Multiple choice

Ratio between length of two trains is 6 : 7 , while speeds of longer trains and smaller train are 72 km/hr & 108 km/hr respectively. If both trains crosses each other running is opposite direction in 10.4 sec, then find in what time longer train will be cross a platform whose length is 520 m ?

  1. 35sec

  2. 25sec

  3. 45sec

  4. 40sec

  5. 55sec
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Convert speeds: 72 km/h = 20 m/s, 108 km/h = 30 m/s. Relative speed = 50 m/s. Total length = 50 * 10.4 = 520 m. Lengths are 6x and 7x, so 13x = 520, x = 40. Longer train length = 7 * 40 = 280 m. Time to cross 520 m platform = (280 + 520) / 20 = 800 / 20 = 40 seconds.

AI explanation

Let the lengths of the shorter and longer trains be 6x and 7x respectively. Their relative speed in opposite directions is (72 + 108) = 180 km/hr, which converts to 180 x (5/18) = 50 m/s. Using the formula Time = Total Distance / Relative Speed, we get 10.4 = (6x + 7x) / 50, yielding a total length of 13x = 520 m and making the longer train 7(40) = 280 m long. The longer train crosses a 520 m platform at 72 km/hr (20 m/s), requiring (280 + 520) / 20 = 40 seconds. The result is 40sec.

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