# Aptitude - Problems on Trains

### Exercise :: Problems on Trains - Data Sufficiency 1

Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is / are sufficient to answer the given question. Read the both statements and

• Give 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.
• Give answer (B) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
• Give answer (C) if the data either in Statement I or in Statement II alone are sufficient to answer the question.
• Give answer (D) if the data even in both Statements I and II together are not sufficient to answer the question.
• Give answer(E) if the data in both Statements I and II together are necessary to answer the question.
1.

 What is the speed of the train whose length is 210 metres? I. The train crosses another train (Howrah Express/12869) of 300 metres length running in opposite direction in 10 seconds. II. The train crosses another train (Howrah Express/12869) running in the same direction at the speed of 60 km/hr in 30 seconds.

 A. I alone sufficient while II alone not sufficient to answer B. II alone sufficient while I alone not sufficient to answer C. Either I or II alone sufficient to answer D. Both I and II are not sufficient to answer E. Both I and II are necessary to answer

Explanation:

 Time taken to cross the train, running in opposite directions = (l1 + l2) sec. (u + v)

 10 = (210 + 300) (u + v)

u + v = 51.

 Time taken to cross the train, running in same direction = (l1 + l2) sec. (u - v)

 30 = (210 + 300) (u - 60 x (5/18))

 u = 17 + 50 m/sec. 3

Thus, u and v can be obtained.

2.

 What is the length of a running train crossing another 180 metre long train running in the opposite direction? I. The relative speed of the two trains was 150 kmph. II. The trains took 9 seconds to cross each other.

 A. I alone sufficient while II alone not sufficient to answer B. II alone sufficient while I alone not sufficient to answer C. Either I or II alone sufficient to answer D. Both I and II are not sufficient to answer E. Both I and II are necessary to answer

Explanation:

Let the two trains of length a metres and b metres be moving in opposite directions at u m/s and v m/s.

 Time taken to cross each other = (a + b) sec. (u + v)

 Now, b = 180, u + v = 150 x 5 m/sec = 125 m/sec. 18 3

 9 = a + 180 (125/3)

a = (375 - 180) = 195 m.

3.

 What is the length of a running train? I. The train crosses a man in 9 seconds. II. The train crosses a 240 metre long platform in 24 seconds.

 A. I alone sufficient while II alone not sufficient to answer B. II alone sufficient while I alone not sufficient to answer C. Either I or II alone sufficient to answer D. Both I and II are not sufficient to answer E. Both I and II are necessary to answer

Explanation:

 Time taken by train to cross a man = Length of train Speed = l ....(i) Speed of train 9

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

 From (i) and (ii), we get l = l + 240 . 9 24

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