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Two trains A and B cross each other in 12 seconds when they move towards each other. The speeds of trains A and B are 81 km/h and 54 km/h respectively. The length of train A is 150 metres more than the length of train B. Which of the following can be obtained from the above information? (i) Time taken by train B to cross a man moving in the same direction as train B. (ii) Time taken by train A to cross a platform of half its length. (iii) Length of train A. (iv) Speed of another train C whose length is equal to the average of the lengths of trains A and B.

1. (i) and (iii)
2. (i), (ii) and (iii)
3. (ii) and (iii)
4. All (i), (ii), (iii) and (iv)

Correct answer: (ii) and (iii)

Solution

The relative speed is 81 + 54 = 135 km/h = 37.5 m/s, so the combined length is 37.5 × 12 = 450 m. With A = B + 150 and A + B = 450, we get A = 300 m and B = 150 m, so (iii) is obtainable. Using A's length, the time to cross a platform of half its length can also be found, so (ii) is obtainable; the other two need additional data.

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