Problems on Trains - Aptitude Questions and Answers - RejinpaulPlacement

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1.
A train crosses a signal post in x seconds. What is the length of the train? [NABARD 2002]

I. The train crosses a platform of 100 metres in y seconds.
II.The train is running at the speed of 80 km/hr.
Answer: (C) if the data either in Statement I or in Statement II alone are sufficient to answer the question

Solution:   Let the length of the train be a metres.

Time taken to cross a signal post = Length of the train / Speed of the train

=> x = l / speed ……… (i)

Time taken to cross the platform = ( l + 100) / Speed
=> y = (l + 100) / Speed ………… (ii)

Thus, from (i) and (ii), we find l.
Also, II gives, speed = [80 * (5/18)] m/sec = 200/9 m/sec

Thus, the data in I or II alone are sufficient to answer the question.

The correct answer is ( c )
2.
What was the speed of the running train? [ Bank P.O 2000]

I. Length of train was 120 metres.
II. The train crossed the other stationary train whose length was 180 m in 4 seconds.
Answer: (E) if the data in both Statement I and II together are necessary to answer the question.

Solution:   Speed of the first train = (sum of the lengths of the two trains) / time taken
= (120 + 180) / 4 m/sec
= 75 m/s

So, both the statements are necessary to get the answer.

Therefore, the correct answer is (e).
3.
What is the speed of the running train which takes 9 seconds to cross a signal post? [Bank P.O 1999]

I. The length of the train is 90 metres.
II. The train takes 27 seconds to cross a platform of 180 metres.

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.

Solution:   Speed of the train = Length of the train / Time taken to cross the post
= 90/9 m/sec
= 10 m/sec.

Thus, I alone gives the answer.

Time taken to cross a platform
= (Length of the train + Length of the platform) / Speed of the train

=> Speed = (l + 180) / 27

But , l is not given. So, speed cannot be obtained.
So, II alone does not give the answer.

The correct answer is (a)
4.
What is the length of the running train? [S.B.I.P.O 1998}

I. The train crosses a man in 9 seconds.
II.The train crosses a 240 metre long platform in 24 seconds.

Answer: (E) if the data in both Statement I and II together are necessary to answer the question.

Solution:   Time taken by train to cross a man = Length of the train / Speed of the train
=> Speed = l / 9 ......... (i)

Time taken by train to cross a platform = (Length of train + Length of Platform) / Speed of the train
=> Speed = (l + 240) / 24 .........(ii)

From (i) & (ii), we get l /9 = (l + 240) / 24

Thus, l can be obtained.
So, I and II are necessary to get the answer.

The correct answer is (e).
5.
What is the speed of the train whose length is 210 metres? [Bank P.O 2003]

I. The train crosses another train of 300 metres length running in opposite direction in 10 seconds.
II.The train crosses another train running in the same direction at the speed of 60 km/hr in 30 seconds.