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    Question

    Two trains, Train X and Train Y, are traveling towards each other on parallel tracks between Stations A and B. How long will it take for Train X to meet Train Y?

    Statements:

    1. Train X is traveling at a speed of 60 km/h and left Station A 30 minutes before Train Y left Station B. The distance between Station A and Station B is 300 km.
    2. Train Y is traveling at 80 km/h.

    A Statement 1 alone is sufficient, but statement 2 alone is not sufficient. Correct Answer Incorrect Answer
    B Statement 2 alone is sufficient, but statement 1 alone is not sufficient. Correct Answer Incorrect Answer
    C Both statements together are sufficient, but neither alone is sufficient. Correct Answer Incorrect Answer
    D Each statement alone is sufficient. Correct Answer Incorrect Answer
    E Statements 1 and 2 together are not sufficient. Correct Answer Incorrect Answer

    Solution

    Solution: From Statement 1: We know Train X's speed (60 km/h), the distance (300 km), and that Train X left 30 minutes (or 0.5 hours) before Train Y. However, we don’t know Train Y's speed, which is necessary to calculate when they will meet. Therefore, Statement 1 alone is not sufficient. From Statement 2: We only know Train Y’s speed (80 km/h), but this alone does not give us enough information to determine when the two trains will meet. Statement 2 alone is not sufficient. Combining Statements 1 and 2: With Train X's speed (60 km/h) and Train Y's speed (80 km/h), and knowing Train X left 0.5 hours before Train Y, we can set up an equation based on their relative distance and speeds to determine when they will meet. Let the time taken after Train Y’s departure for the two trains to meet be t. Train X would have covered 60 * 0.5 = 30 km by the time Train Y departs. Now, the remaining distance is 300 - 30 = 270 km, which they cover together at a relative speed of 60 + 80 = 140 km/h. Thus, t = 270 / 140 = 1.93 hours. Therefore, both statements together are sufficient. Correct Answer: (c) Both statements together are sufficient, but neither alone is sufficient.

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