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Problems on Trains - General Aptitude

Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.
Q1:

What is the speed of the train?
I.  The train crosses a signal pole in 18 seconds.
II.  The train crosses a platform of equal length in 36 seconds.
 III.  Length of the train is 330 metres.

A I and II only

B II and III only

C I and III only

D III and either I or II only

E Any two of the three

ANS:D - III and either I or II only

Let the speed of the train be x metres/sec.

Time taken to cross a signal pole = Length of the train
Speed of the train
Time taken to cross a platform = (Length of the train + Length of the Platform)
Speed of the train
Length of train = 330 m.
I and III give, 18 = 330     x = 330 m/sec = 55 m/sec.
x 18 3
II and III give, 36 = 2 x 330      x = 660 m/sec = 55 m/sec.
x 36 3
 Correct answer is (D).