# Train Problems Data Sufficiency

## Train Problems Data Sufficiency

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 trainto 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.

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
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.
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.
Explanation:
From the statement I, we get length of the train is 200 metres (Redundant info while comparing with Statement III). The rest of the info given in this statement cannot be used for calculating the speed of the train, because the two trains might run at different speed.
 III gives, speed = 200 m/sec = 20 m/sec = 20 x 18 km/hr = 72 km/hr. 10 5
 II gives, time taken = 558 hrs = 31 hrs = 7 3 hrs = 7 hrs 45 min. 72 4 4
So, the train will reach city X at 3 p.m.
Hence II and III only gives the answer.
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.