Multiple choice

The lengths of trains A and B are in the ratio 2:3. Which of them takes less time to cross the same platform? Statement I : The time taken by train A to cross train B when they are moving in opposite directions is half the time taken by it to cross train B, when moving in the same direction. Statement II : The ratio of the length of train B to that of the platform is 4 : 3.

  1. If the data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question

  2. If the data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question

  3. If the data either in statement I alone or in statement II alone is sufficient to answer the question

  4. If the data in both statements I and II together are necessary to answer the question

  5. If the data given in both statements I and II together are not sufficient to answer the question.
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A Correct answer
Explanation

Statement I provides the relative speeds in both directions, which allows comparing the time taken to cross another train. Statement II only gives a ratio of lengths, which is insufficient to determine time without speed information.

AI explanation

Let the lengths of trains A and B be 2x and 3x, and their speeds be a and b. Statement I provides the equation (2x + 3x) divided by the sum of a and b equals one half of 5x divided by the difference of a and b, which simplifies to the ratio of a to b being 3. This gives the exact speed ratio needed to determine which train is faster and takes less time to cross the platform. Statement II only relates the train length to the platform length without providing any speeds, so it is insufficient; the data in statement I alone is sufficient to answer the question.

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