Quantitative Aptitude

Problems on Trains

989 Questions
All Passing a moving person or another train 430 Crossing a platform or bridge 379 Crossing a pole or stationary person 104 Meeting point and post-meeting times 52 Journey time, reduced speed, and schedule conditions 24

Problems on Trains Questions

Multiple choice

Anju is waiting on the railway station for the arrival of her train. Two trains running in opposite directions cross Anju on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speed is

  1. 2 : 3

  2. 1 : 2

  3. 3 : 2

  4. 2 : 1
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let lengths be L1, L2 and speeds be v1, v2. L1/v1 = 27, L2/v2 = 17. (L1+L2)/(v1+v2) = 23. Substituting L1=27v1 and L2=17v2: (27v1 + 17v2)/(v1+v2) = 23. 27v1 + 17v2 = 23v1 + 23v2. 4v1 = 6v2. v1/v2 = 6/4 = 3/2.

Multiple choice

Directions: In this problem, a question is followed by three statements, labelled as (A), (B) and (C). Read the statements carefully and determine which of them is/are sufficient/necessary to answer the question. What is the length of the platform? (A) The train crosses a woman standing on the platform in 35 seconds. (B) The train passes a station platform in 50 seconds and speed of the train is 72 km/hr. (C) The length of the train is 700 m.

  1. Any one of them is sufficient.

  2. Only A and C together are sufficient.

  3. Only A and B together are sufficient.

  4. Either A alone or B alone is sufficient.

  5. All A, B and C are necessary.
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

Directions: The question below is followed by statements A and B. You have to decide whether the data provided in the statements is sufficient to answer the question. Read both the statements and choose the correct alternative. What are the speeds of two trains 80 m and 85 m long? (A) They take 37.5 seconds to pass each other when running in the same direction. (B) They take 7.5 seconds to pass each other when running in opposite directions.

  1. Statement (A) alone is sufficient, but statement (B) alone is not sufficient.

  2. Statement (B) alone is sufficient, but statement (A) alone is not sufficient.

  3. Both (A) and (B) together are sufficient, but neither of them alone is sufficient.

  4. Each statement alone is sufficient.

  5. Statements (A) and (B) together are not sufficient.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let speeds be v1 and v2. (A) (80+85)/(v1-v2) = 37.5. (B) (80+85)/(v1+v2) = 7.5. We have two equations with two variables, so both are needed to solve for v1 and v2.

Multiple choice

Directions: In the following item, a question is followed by data in the form of two statements labelled as I and II. You have to decide whether the data given in the statements is sufficient to answer the question. Using the data, make an appropriate choice from [1] to [4] as per the following guidelines: Mark choice [1] if statement I alone is sufficient to answer the question. Mark choice [2] if statement II alone is sufficient to answer the question. Mark choice [3] if both statements I and II are sufficient to answer the question, but neither statement alone is sufficient. Mark choice [4] if both statements I and II together are not sufficient to answer the question and additional data is required. What is the speed of the train? I. The length of the train is 100 metres. II. The train passes the other stationary train, whose length is 150 metres, in 5 seconds.

  1. 1

  2. 2

  3. 3

  4. 4

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Speed = Distance / Time. Statement I gives the length of the train. Statement II gives the length of the other train and the time taken to pass it. Together, the total distance is 100 + 150 = 250 metres, and time is 5 seconds, so speed = 250 / 5 = 50 m/s. Both are required.

Multiple choice

A train X of length L m crosses train Y of length (L + 15) m running in from opposite direction in 11 sec. If the speed of train X is S km/hr and the speed of train Y is (S + 18) km/hr, then train X will cross a tunnel of length 360 m in 30 seconds. What can be found from the given data? (i) Time taken to cover (L + 60) m at the speed of (S + 8) km/hr (ii) Ratio of the time taken to cover distance '(L + 10)' m at the speed of 'S' to time taken to cover distance '(L - 40)' m at the speed of '(S + 28)' km/hr (iii) The speed of train X at which a tunnel of length 300 m is crossed in 10 s (iv) Distance covered in 20 min at the speed of (S + 12) km/h

  1. Only (i) and (ii)

  2. Only (ii) and (iii)

  3. Only (i), (iii) and (iv)

  4. (i), (ii), (iii) and (iv)

  5. Only (i) and (iv)
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The given data allows solving for L and S using the two time equations (crossing train Y and crossing the tunnel). Once L and S are known, all listed quantities (i) through (iv) can be calculated.

Multiple choice

A train 'A' travelling at a speed of S km/hr leaves from a station X and another train 'B' travelling at a speed of (S + 30) km/hr leaves the same station X after 10 hours in the same direction. Train A meets train B after 1800 km. Which of the following can be obtained from the above given information? (i) Time taken by train A to cross a platform of length 140 m (ii) Time taken by train B to cross a man moving in the same direction as of train A (iii) Speed of train B (iv) Distance travelled by train B in 5 hours

  1. Only (iii) and (iv)

  2. Only (i), (ii) and (iv)

  3. Only (i), (ii) and (iii)

  4. Only (i) and (iv)

  5. All (i), (ii), (iii) and (iv)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Train A speed S, Train B speed S+30. Train B leaves 10h later. Train A meets B at 1800km. Time A = 1800/S. Time B = 1800/(S+30). Time A - Time B = 10. 1800/S - 1800/(S+30) = 10. 180/S - 180/(S+30) = 1. 180(30) = S(S+30). S^2 + 30S - 5400 = 0. (S+90)(S-60) = 0. S = 60. Speed B = 90. We know speeds, so we can find (iii) and (iv).

Multiple choice

Directions: The question given below is followed by two statements I and II. You have to determine whether the data given in the statement is sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose the best possible answer. How many seconds will Train A, running at 90 km/h, take to completely cross a man going in the opposite direction on the platform? (I) Speed of the man is 7.2 km/h. (II) It takes 27 seconds for the train to completely cross the same man, if going in the same direction.

  1. The question can be answered by using statement I alone but cannot be answered using the other statement alone.

  2. The question can be answered by using statement II alone but cannot be answered using the other statement alone.

  3. The question can be answered by using either of the statements alone.

  4. The question can be answered using both of the statements together, but cannot be answered using either of the statements alone.

  5. The question cannot be answered even by using both the statements together.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To find the time taken to cross the man, we need the relative speed and the length of the train. Statement I gives the man's speed, and Statement II provides the time taken when moving in the same direction, which allows us to calculate the train's length using the relative speed formula. Both statements are required to determine the length of the train and subsequently the time taken to cross the man in the opposite direction.

Multiple choice

Directions: In the following problem, a question is followed by three statements numbered (I), (II), and (III). Read the statements carefully and determine which of the given statements is/are sufficient/necessary to answer the question. At what speed did train cross the platform? I. Length of the platform is 120 m. II. Train crossed the platform in 8 seconds. III. Length of the platform and the train altogether is equal to 200 m.

  1. Only statements I and II

  2. Only statements I and III

  3. Only statements II and III

  4. All three statements

  5. Only statement II and either statement I or statement III
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To find the speed, we need the total distance (length of train + length of platform) and the time taken. Statement II gives time. Statement III gives the total distance. Statement I is redundant if III is known. Thus, II and III are sufficient.

Multiple choice

Directions: Compare Quantity I and Quantity II, using additional information centred above the two quantities if such information is given, and choose the correct option. Quantity I: Value of the length of train B in metres, if train A of length 150 m starts from a point and runs at constant speed of 90 km/hr; after 20 seconds, train B of different length starts from the same point on a parallel track to chase train A at a speed of 126 km/hr and crosses it completely in 20 seconds Quantity II: Value of the perimeter of the field in meters, if a rectangular field has area 2000 m2, the length of which is 10 m more than its width

  1. Quantity I = Quantity II or no relation

  2. Quantity I > Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I < Quantity II

  5. Quantity I ≤ Quantity II
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

Directions: In the given question, two quantities are given, one as 'Quantity 1' and another as 'Quantity 2'. You have to determine the relationship between the two quantities and choose the appropriate option. A 251 m long train crosses a bridge in 10 seconds. Quantity 1: Value of (x + 25 % of x), If speed of the train is x and the length of the bridge is 149 m Quantity 2: Value of (2y + 10 % of y), If speed of the train is y and the length of the bridge is 159 m

  1. Quantity 1 > Quantity 2

  2. Quantity 1 ≥ Quantity 2

  3. Quantity 2 > Quantity 1

  4. Quantity 2 ≥ Quantity 1

  5. Quantity 1 = Quantity 2 or Relation cannot be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Speed = (Length of train + Length of bridge) / Time. For Q1: x = (251 + 149) / 10 = 40. Value = 40 + 0.25*40 = 50. For Q2: y = (251 + 159) / 10 = 41. Value = 2(41) + 0.1*41 = 82 + 4.1 = 86.1. Since 86.1 > 50, Q2 > Q1.