Multiple choice

Passage

Directions : The question given below is followed by two statements I and II. You are to determine whether the data given in the statement is sufficient to answer the question. You should use the data and your knowledge of Mathematics to choose between the possible answers. Give answer according to the following codes: (a) If the question can be answered by using statement I alone but cannot be answered by using statement II alone. (b) If the question can be answered by using statement II alone but cannot be answered by using statement I alone. (c) If both statements I and II together are required to answer the question. (d) If the answer can be found by using any of the two statements alone. (e) If both the statements together are not sufficient to answer the question.

Two trains moving in opposite directions are crossing each other. If train1 crosses train2 moving at the speed of 162 km/hr, find the length of train1. I. Train1 crosses train2 of length 160 m in 4 seconds. II. Train1 moving at the speed of 144 km/hr crosses train2 of length 160 m in 4 seconds.

  1. (a)

  2. (b)

  3. (c)

  4. (d)

  5. (e)
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B Correct answer
Explanation

To find the length of train 1, we need its speed and the relative speed. Statement I gives time and length of train 2 but not speed of train 1. Statement II gives the speed of train 1 (144 km/hr) and the length of train 2 (160 m) and the time (4 seconds). Using relative speed (144 + 162 = 306 km/hr = 85 m/s), we can find the total length (160 + L1 = 85 * 4 = 340), so L1 = 180 m. Thus, II alone is sufficient.

AI explanation

To find the length of the first train, we need the relative speed of the two trains and the crossing time. The second statement gives the first train's speed as 144 km/hr, which combines with the given 162 km/hr to yield a relative speed of 306 km/hr or 85 m/s. Using the crossing time of 4 seconds and the second train's length of 160 m, the first train's length is calculated as (85 * 4) - 160 = 180 m. Since the first statement lacks the first train's speed, the question can be answered by using statement II alone but cannot be answered by using statement I alone.

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