# Aptitude - Problems on Trains

### Exercise :: Problems on Trains - Data Sufficiency 2

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

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

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. 7

Thus I and II give the speed of the train. The correct answer is (A.)