Multiple choice

Two trains running in opposite directions cross a stationary man on the platform in 72 seconds and 48 seconds, respectively. The time taken by the trains to cross each other completely is 60 seconds. What is the respective ratio of their speeds?

  1. 9 : 1

  2. 3 : 2

  3. 2 : 3

  4. 1 : 1

  5. None of these
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D Correct answer
Explanation

Let speeds be v1 and v2. Lengths are L1 = 72v1 and L2 = 48v2. Time to cross each other is (L1 + L2) / (v1 + v2) = 60. Substituting: (72v1 + 48v2) / (v1 + v2) = 60. 72v1 + 48v2 = 60v1 + 60v2. 12v1 = 12v2, so v1/v2 = 1/1.

AI explanation

Let the speeds be v1 and v2, and the lengths be L1 and L2. We know L1 equals 72*v1 and L2 equals 48*v2. Using the formula for objects moving in opposite directions, 60 = (L1 + L2)/(v1 + v2). Substituting the lengths gives 60 = (72*v1 + 48*v2)/(v1 + v2), which simplifies to 72*v1 + 48*v2 = 60*v1 + 60*v2 and results in 12*v1 = 12*v2, making their ratio 1:1.

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