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 300 m. long is running at a speed of 35 km/hr. Another train 200 m. long is coming from opposite direction at a speed of 25 km/hr.Then what is the time taken by trains to cross each other is?

  1. 20 sec.

  2. 30 sec.

  3. 45 sec.

  4. 60 sec.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When two trains cross each other from opposite directions, their relative speed is the sum of their individual speeds. Total distance to be covered is the sum of both train lengths (300 + 200 = 500m). Relative speed = 35 + 25 = 60 km/hr = 60 × 5/18 = 50/3 m/s. Time = Distance/Speed = 500 ÷ (50/3) = 30 seconds. Option A (20 sec) is incorrect - it would require a much higher relative speed.

Multiple choice

What is the length of a train? (I) The train crosses a 364 metre long platform in 24 seconds. (II) The train crosses a man standing on the platform in 10 seconds. (III) The speed of the train is 72 km./hr.

  1. Only I and II

  2. All I, II and III

  3. Any two of the three

  4. Only I and III

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

For train length problems, we need speed and time to cross a known distance. Statement I gives platform length and crossing time, yielding train length if speed is known. Statement II gives time to cross a person (effectively the train's own length at that speed). Statement III gives speed directly. Any two statements together provide sufficient information: I+II uses relative motion, I+III or II+III use explicit speed.

Multiple choice

A train crosses a platform in 25 seconds. The length of the platform is 260 metres. What is the length of the train?

  1. 420m

  2. 450m

  3. 480m

  4. Cannot be determined

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

To find the length of the train, we need both the time taken to cross the platform AND the speed of the train. The distance covered when a train crosses a platform equals (train length + platform length). Here we only know the time (25 seconds) and platform length (260m), but the train's speed is unknown. Without speed or any additional information (like the time to pass a pole), we cannot determine the train's length uniquely.

Multiple choice

A train crossed a platform in 30 seconds. The length of the platform is 300 metres. What is the length of the train?

  1. 200 metre

  2. 250 metre

  3. 300 metre

  4. Cannot be determined

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

To cross a platform, the train must cover its own length plus the platform's length. We know the crossing time (30s) and platform length (300m), but without the train's speed, we cannot find the train's length. Two unknowns (train length and speed) cannot be solved with one equation.

Multiple choice

A train running at a certain speed crosses a 300 m and 240 m long bridges in 21 seconds and 18 seconds respectively. What is the speed of the train?

  1. 72 km/hr

  2. 68 km/hr

  3. 65 km/hr

  4. 60 km/hr

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

Let train length = L meters and speed = S m/s. Crossing bridge means L + bridge_length = S × time. So: L + 300 = 21S and L + 240 = 18S. Subtract: 60 = 3S, so S = 20 m/s = 20 × (18/5) = 72 km/hr. Option A (72 km/hr) is correct. The train length is L = 21×20 - 300 = 120 m, which checks out.

Multiple choice

What is the speed of a train? (I) The train crosses a man in 10 seconds. (II) The train crosses a 300 metre long platform, which is equal to its length in 30 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
B Correct answer
Explanation

Statement II: Train crosses 300m platform (equal to its length) in 30s. So train length = 300m, total distance = 600m. Speed = 600/30 = 20 m/s. Statement I alone doesn't give length, so insufficient. Option B (II alone sufficient) is correct.

Multiple choice

A train 125 m. in length, moves at a speed of 82 km/hr. In what time the train will cross a boy who is walking at 8 km./hr. in opposite direction?

  1. 8 sec.

  2. 9 sec.

  3. 5 sec.

  4. 6 sec.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When two objects move in opposite directions, their relative speed is the sum of their individual speeds. The train's speed is 82 km/hr and the boy walks at 8 km/hr in opposite direction, so relative speed = 82 + 8 = 90 km/hr = 25 m/s. Time to cross = distance / relative speed = 125/25 = 5 seconds. The boy's motion is opposite to the train, so they approach each other faster than if the boy were stationary.

Multiple choice

A train 110 m long is running with a speed of 60 km/hr. What is the time in which it will pass a man who starts from the engine running at the speed of 6 km/hr in the direction opposite to that of the train?

  1. 5 sec.

  2. 6 sec.

  3. 10 sec.

  4. 15 sec.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Relative speed = 60 + 6 = 66 km/hr = 66 × 1000/3600 = 55/3 m/s. The train must cover its own length of 110 m relative to the man. Time = distance/speed = 110/(55/3) = 6 seconds. This makes sense because they're moving toward each other, increasing effective speed.

Multiple choice

A 476 m long train crosses a pole in 14 seconds. The length of a platform is equal to the distance covered by train in 20 seconds. A man crosses the platform in 7 minutes and 5 seconds. What is the speed of man in m/s?

  1. 1.8 m/s

  2. 1.4 m/s

  3. 1.6 m/s

  4. 2 m/s

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

Train length = 476 m, crosses pole in 14 seconds. Speed = 476/14 = 34 m/s. In 20 seconds, train covers 34 × 20 = 680 m = platform length. Man crosses 680 m in 7 minutes 5 seconds = 425 seconds. Man's speed = 680/425 = 1.6 m/s.

Multiple choice

Train A crosses a platform in 30 seconds. What is the speed of Train A? I. Train A crosses a 180 m. long train running in opposite direction in 36 seconds. II. The other train crosses a signal in 9 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
D Correct answer
Explanation

Statement I: Train A crosses 180m train in 36 seconds. But we don't know the other train's speed or Train A's length. Not sufficient. Statement II: Other train crosses a signal in 9 seconds. This gives the other train's length, but not Train A's details. Even together, we can't find Train A's speed because we don't know Train A's length from crossing a platform. Insufficient.

Multiple choice

A 200 m long train crosses a man standing on a 300 m long running train. If the speeds of the trains are 30 km/h and 40 km/h, find the time taken for the first train to cross the man.

  1. 10 sec

  2. 15 sec

  3. 20 sec

  4. Can't be determined

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

The time depends on whether the trains are moving in the same or opposite directions, which isn't specified. If same direction: relative speed = 10 km/h, time = 200/(10*5/18) = 72 sec. If opposite: relative speed = 70 km/h, time = 200/(70*5/18) = 10.3 sec. Since both scenarios are possible and neither matches options A-C, 'Can't be determined' is correct.

Multiple choice

A train having length 250 m. is running with the speed of 72 km/h, another train having length 300 m. come from opposite direction and crosses the first train in 25 sec. Find the speed of second train?

  1. 7.2

  2. 3.6

  3. 3.7

  4. 6.5

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

Train 1: length = 250 m, speed = 72 km/h = 20 m/s. Combined length = 250 + 300 = 550 m. Time to cross = 25 sec. Relative speed = 550/25 = 22 m/s. If trains are opposite: 20 + v = 22 → v = 2 m/s = 7.2 km/h. Option A is correct. If same direction, v would be negative (impossible), so opposite is implied.

Multiple choice

A train required 7 seconds to pass a pole while it requires 25 seconds to cross a stationary train which is 378 m long. What is the speed of train?

  1. 75.6 km/hr

  2. 75.4 km/hr

  3. 76.2 km/hr

  4. 21 km/hr

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

Time to pass pole = 7 seconds = train length / speed. So train length = 7v. Time to cross stationary train = 25 seconds = (train length + 378) / speed. So 7v + 378 = 25v, meaning 18v = 378, so v = 21 m/s. Convert to km/hr: 21 × (18/5) = 75.6 km/hr. Option A is correct.

Multiple choice

Two trains 132 metres and 108 metres in length are running towards eachother on parallel lines, one at the rate of 32 km/hr and another 40 km/hr. Then time taken by the trains in passing each other -

  1. 15 second

  2. 12 second

  3. 18 second

  4. 20 second
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When trains move toward each other, their relative speed is the sum of individual speeds: 32 + 40 = 72 km/hr. Total distance to cover = 132 + 108 = 240 m = 0.24 km. Time = Distance/Speed = 0.24/72 hours = 0.00333 hours. Converting to seconds: 0.00333 × 3600 = 12 seconds. This uses the formula for relative speed when objects move in opposite directions.