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What is the speed of the train whose length is 420 metres? I. The train crosses another train of 600 metres length running in opposite direction in 20 seconds. II. The train crosses another train running in the same direction at the speed of 50/3 m/sec in 60 seconds.

1. Statement I alone is sufficient
2. Statement II alone is sufficient
3. Both statements together are sufficient, but neither alone is sufficient
4. Each statement alone is sufficient

Correct answer: Both statements together are sufficient, but neither alone is sufficient

Solution

Statement I alone: (420+600)/20 = 51 = speed of train + speed of other train (opposite direction). Two unknowns, one equation. Insufficient alone. Statement II alone: length of the other train (same direction) is unknown. Can't solve. Together: if we use the 2nd train's speed (50/3 m/s) from Statement II as one of the two speeds from Statement I (i.e., v2=50/3), then v1=51-50/3=(153-50)/3=103/3 m/s. Alternatively, treating the second train in II as having speed 50/3 m/s and its length being inferable: both statements together give enough to solve. Answer: Both together are sufficient.

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