 ## Problems on Trains - Important Formulas

1. km/hr to m/s conversion:

a km/hr = a x 5 m/s.18

2. m/s to km/hr conversion:

a m/s = a x 18 km/hr.5

3. Formulas for finding Speed, Time and Distance

4. Time taken by a train of length l metres to pass a pole or standing man or a signal post is equal to the time taken by the train to cover l metres.

5. Time taken by a train of length l metres to pass a stationery object of length b metres is the time taken by the train to cover (l + b) metres.

6. Suppose two trains or two objects bodies are moving in the same direction at u m/s and v m/s, where u > v, then their relative speed is = (u - v) m/s.

7. Suppose two trains or two objects bodies are moving in opposite directions at u m/s and v m/s, then their relative speed is = (u + v) m/s.

8.If two trains of length a metres and b metres are moving in opposite directions at u m/s and v m/s, then: The time taken by the trains to cross each other = (a + b) sec.(u + v)

9. If two trains of length a metres and b metres are moving in the same direction at u m/s and v m/s, then: The time taken by the faster train to cross the slower train = (a + b) sec.(u - v)

10. If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then: (A's speed) : (B's speed) = (b : a)

## Problems on Trains - General Questions

1. A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?

• A. 120 metres
• B. 180 metres
• C. 324 metres
• D. 150 metres

2. A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:

• A. 45 km/hr
• B. 50 km/hr
• C. 54 km/hr
• D. 55 km/hr

3. The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:

• A. 200 m
• B. 225 m
• C. 245 m
• D. 250 m

4. Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:

• A. 1 : 3
• B. 3 : 2
• C. 3 : 4
• D. None of these

5. A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?

• A. 120 m
• B. 240 m
• C. 300 m
• D. None of these

6. A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?

• A. 65 sec
• B. 89 sec
• C. 100 sec
• D. 150 sec

7. Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is:

• A. 50 m
• B. 72 m
• C. 80 m
• D. 82 m

8. A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?

• A. 40 sec
• B. 42 sec
• C. 45 sec
• D. 48 sec

9. Two trains are moving in opposite directions @ 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is:

• A. 36
• B. 45
• C. 48
• D. 49

10. A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?

• A. 3.6 sec
• B. 18 sec
• C. 36 sec
• D. 72 sec

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

Directions to Solve

• 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

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

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

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

Directions to Solve

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

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

## Exercise :: Problems on Trains - Data Sufficiency 3

Directions to Solve

Each of these questions is followed by three statements. You have to study the question and all the three statements given to decide whether any information provided in the statement(s) is redundant and can be dispensed with while answering the given question.

1. At what time will the train reach city X from city Y?
I. The train crosses another train of equal length of 200 metres and running in opposite directions in 15 seconds.
II. The train leaves city Y and 7.15 a.m. for city X situated at a distance of 558 km.
III. The 200 metres long train crosses a signal pole in 10 seconds.

• A. I only
• B. II only
• C. III only
• D. II and III only
• E. All I, II and III are required.

2. What is the length of a running train P crossing another running train Q?
I. These two trains take 18 seconds to cross each other.
II. These trains are running in opposite directions.
III. The length of the train Q is 180 metres.

• A. I only
• B. II only
• C. III only
• D. All I, II and III are required
• E. Even with I, II and III, the answer cannot be obtained.