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

A train running at uniform speed crosses 600 m and 300 m long two bridges in 2 minutes and 80 seconds respectively. What is the speed of the train?

  1. 27 km/hr

  2. 42 km/hr

  3. 36 km/hr

  4. 48 km/hr

  5. 84 km/hr
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let train length = L meters and speed = S m/s. For first bridge: (L+600)/S = 120 seconds (2 min). For second bridge: (L+300)/S = 80 seconds. Solving: L+600 = 120S and L+300 = 80S. Subtracting: 300 = 40S, so S = 7.5 m/s = 27 km/hr. This matches option A.

Multiple choice

How long does a train take to cross another train? I. A train 110 metres long travels at 60 km./hr. II. Another train is 180 metres long. III. Speed of another train is 54 km./hr.

  1. Only I and II

  2. Only I and III

  3. Only II and III

  4. All I, II and III

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

To find crossing time, we need both train lengths and their speeds. The formula uses total distance (sum of lengths) divided by relative speed. Statement I gives length and speed of first train, II gives length of second train, and III gives speed of second train. All three are required to calculate the crossing time.

Multiple choice

Two trains, 125 metres and 115 metres in length, are running towards each other on parallel lines, one at the rate of 33 km/hr. and the other at 39 km/hr. How much time (in second) will they take to pass each other from the moment they meet?

  1. 8

  2. 10

  3. 12

  4. 15

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

When trains move toward each other, their relative speed is the sum: 33 + 39 = 72 km/hr. Convert to m/s: 72 × (5/18) = 20 m/s. Total distance to cover = sum of lengths = 125 + 115 = 240 m. Time = Distance/Speed = 240/20 = 12 seconds.

Multiple choice

What is the speed of train X? I. Train X crosses 140 m. long train Y moving in opposite direction in 10 seconds. II. Train X crosses 400 m. long platform in 28 seconds. III. Train X crosses a man standing on the platform in 8 seconds.

  1. I and II

  2. II and III

  3. I and III

  4. Any of two

  5. Can't given the answer included three statement also
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement II gives: Length of train X + 400 = 28 × speed of train X. This alone cannot give the speed. Statement III gives: Length of train X = 8 × speed of train X. From III, speed = Length/8. Substituting in II: Length + 400 = 28 × (Length/8) = 3.5 × Length, so 400 = 2.5 × Length, Length = 160 m, Speed = 160/8 = 20 m/s. Statements II and III together are sufficient. Statement I is not needed as we don't need train Y's details.

Multiple choice

What is the speed of a train? Statement I: The train crosses a pole in 10 seconds. Statement II: The train crosses a 200 meter long platform in 20 seconds.

  1. If statement I alone is sufficient but statement II alone is not sufficient.

  2. If statement II alone is sufficient but statement I alone is not sufficient.

  3. If each statement alone (either I or II) is sufficient.

  4. If statement I and II together are not sufficient.

  5. If both statements I and II together are sufficient, but neither statement alone is sufficient.
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Statement I: Train crosses a pole in 10 seconds. This means the train covers its own length in 10 seconds, so speed = length/10. But we don't know length. Statement II: Train crosses 200m platform in 20 seconds, meaning train covers (length + 200) in 20 seconds. Combining both: length/10 = (length + 200)/20, solving gives length = 200m, then speed = 200/10 = 20 m/s. Both statements needed.

Multiple choice

Two trains are running in the same direction at 50km/hr. and 30km/hr. The faster train crosses a man sitting in the slower train in 18 seconds. Find the length of the faster train?
  1. $120m$
  2. $125m$
  3. $105m$

  4. Can't be determined

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

Relative speed of faster train w.r.t. slower train = 50 - 30 = 20 km/hr. Convert to m/s: 20 × (1000/3600) = 20 × (5/18) = 100/18 ≈ 5.56 m/s. Time = 18 seconds. Length = Speed × Time = (100/18) × 18 = 100 meters. Since 100m is not in the given options (120, 125, 105), the answer is 'None of these'. Option E is correct.

Multiple choice

The following questions are accompanied by three statements I, II and III. You have to determine which statement(s) is/are necessary/sufficient to answer the question. What is the relative speed of two trains running in opposite direction? (I) The length of each train is 120 m. (II) The speed of one of these trains is 48 km/hr. (III) They take 8 seconds to cross each other.

  1. I,II and III

  2. I & II together

  3. III & either I or II

  4. Only II

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

When trains cross in opposite directions, relative speed = (sum of lengths)/time. Statement III gives time (8 seconds) which is essential. Statement I gives total length (120 + 120 = 240 m) which is essential. Statement II gives one train's speed (48 km/hr) but we need the sum of both speeds. However, if we interpret it as needing all statements to have enough data, we need length and time and at least one speed to find the other. The question asks for relative speed, and with only II, we have insufficient data (missing lengths and time). All three together provide complete information.

Multiple choice

200 meter long train crosses a bridge with the speed of 54 km/hrs. in 30 sec. Find the length of bridge ?

  1. 125 m.

  2. 300 m.

  3. 450 m.

  4. Can't be determined

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

Speed = 54 km/hr = 54 × 5/18 = 15 m/s. In 30 seconds, the train covers 15 × 30 = 450 meters. This equals train length + bridge length. So 450 = 200 + bridge, giving bridge length = 250 meters. Since 250m is not among options A-C, option E (None of these) is correct.

Multiple choice

Two trains A and B are running on parallel tracks in the same direction. Train A which is coming from behind, takes 50 seconds to cross B completely. One person in train A observes that he crosses train B in 30 second. If the speeds of the train A and train B are in the ratio of 2 : 1, what is the ratio of their length?

  1. 7 : 5

  2. 5 : 7

  3. 2 : 3

  4. 3 : 5

  5. 3 : 2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let speeds be 2v and v. Relative speed (same direction) = 2v - v = v. When A crosses B completely: L_A + L_B = v × 50. When person in A observes crossing B: L_B = v × 30. So L_B = 30v, then L_A = 20v. Ratio L_A : L_B = 20 : 30 = 2 : 3. Option C matches.

Multiple choice

A 150 meter long train is running at a speed of 75 km. /hr. In how many seconds it will cross a 90 meter long train running in the opposite direction at a speed of 45 km. /hr.?

  1. 15.2 sec.

  2. 12.4 sec.

  3. 10.3 sec.

  4. 7.2 sec.

  5. 6.1 sec.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total distance = 150 + 90 = 240 m. Relative speed when moving opposite = 75 + 45 = 120 km/hr = 120 × (5/18) = 33.33 m/s. Time = Distance/Speed = 240/33.33 = 7.2 seconds. Option D is correct. This uses relative speed concept and unit conversion.