Aptitude - Problems on Trains

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.

1. 

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

Answer: Option D

Explanation:

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).


2. 

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

Answer: Option A

Explanation:

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.)