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Problems on Trains - General Aptitude

Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is / are sufficient to answer the given question. Read the both statements and
  • Give answer (A) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
  • Give answer (B) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
  • Give answer (C) if the data either in Statement I or in Statement II alone are sufficient to answer the question.
  • Give answer (D) if the data even in both Statements I and II together are not sufficient to answer the question.
  • Give answer(E) if the data in both Statements I and II together are necessary to answer the question.
Q1:

What is the length of a running train crossing another 180 metre long train running in the opposite direction?
I.  The relative speed of the two trains was 150 kmph.
 II.  The trains took 9 seconds to cross each other.

A I alone sufficient while II alone not sufficient to answer

B II alone sufficient while I alone not sufficient to answer

C Either I or II alone sufficient to answer

D Both I and II are not sufficient to answer

E Both I and II are necessary to answer

ANS:E - Both I and II are necessary to answer

Let the two trains of length a metres and b metres be moving in opposite directions at u m/s and v m/s.

Time taken to cross each other = (a + b) sec.
(u + v)
Now, b = 180, u + v = 150 x 5 m/sec = 125 m/sec.
18 3
 9 = a + 180
(125/3)
 a = (375 - 180) = 195 m.