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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 tree in 13 seconds.  II. The train crosses a platform of length 250 metres in 27 seconds.  III. The train crosses another train running in the same direction in 32 seconds.

A I and II only

B II and III only

C I and III only

D Any two of the three

E None of these

ANS:A - I and II only

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

Time taken to cross a tree = 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
I gives, 13 = l      13x.
x
II gives 27 = l + 250
x
13x + 250 = 27
x
 x = 125 m/sec.
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Thus I and II give the speed of the train.  The correct answer is (A.)