Multiple choice

Passage

Directions: The question below is followed by statements I and II. You are to determine whether the data given in the statements is sufficient to answer the question. You should use the data and your knowledge of Mathematics to choose between the possible answers. Give answer (a) if the question can be answered by using statement I alone but cannot be answered by statement II alone (b) if the question can be answered by using statement II alone but cannot be answered by 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

A train crosses a man in 8 seconds. Find the length of the train. I. Same train crosses another slower moving train, going in the same direction, at a speed of 25 m/sec in 20 seconds. II. Length of the slower train is 120 m.

  1. (a)

  2. (b)

  3. (c)

  4. (d)

  5. (e)

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To find the length of the train, we need its speed. Statement I gives the relative speed with another train, but we don't know the speed of the other train. Statement II gives the length of the other train. Together, we have: (L1 + L2) / (V1 - V2) = 20. We know L1/V1 = 8, L2 = 120, V2 = 25. We have two equations with two variables (L1, V1), allowing us to solve for L1.

AI explanation

Let the length of the train be L and its speed be S. From the given information, L equals 8S. Statement I gives the relative speed between the two trains as 25 m/s, so S minus the slower train's speed equals 25. Statement II provides the slower train's length as 120 m, and since the crossing time is 20 seconds, we can write L plus 120 equals 25 multiplied by 20. Neither statement alone can solve for L, but using both together allows you to find L equals 400 m; therefore, both statements I and II together are required to answer the question.