Multiple choice

Two trains each having a length of 160 metres moving in opposite directions crossed each other in 9 seconds. If one train crossed a 200-metre-long platform in 18 seconds, then the ratio of their speeds is:

  1. 2 : 3

  2. 9 : 7

  3. 5 : 8

  4. 3 : 4
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B Correct answer
Explanation

Relative speed = (160+160)/9 = 320/9 m/s. Train 1 speed: (160+200)/18 = 360/18 = 20 m/s. Train 2 speed = 320/9 - 20 = 140/9 m/s. Ratio = 20 : 140/9 = 180/9 : 140/9 = 180:140 = 9:7.

AI explanation

Let the speeds be x m/s and y m/s, so crossing each other in 9 seconds gives (x plus y) equals 320 divided by 9. The first train crossing the 200 m platform gives 18x equals 160 plus 200 equals 360, so x equals 20 m/s. Substituting x into the first equation gives (20 plus y) equals 320/9, so y equals 140/9 m/s. The ratio of their speeds is 20 divided by (140/9) equals 180 divided by 140, which simplifies to 9 : 7.

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