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 crosses a 100 m long platform in 14 seconds and crosses a man standing on the platform in 10 seconds. Find the speed of the train.

  1. 45 km/hr.

  2. 40 km/hr.

  3. 25 km/hr.

  4. 30 km/hr.

  5. 90 km/hr.
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

To find the speed: Let train length = L meters and speed = v m/s. Crossing a 100m platform in 14s means L + 100 = 14v. Crossing a man (train length only) in 10s means L = 10v. Substituting: 10v + 100 = 14v, so 4v = 100, v = 25 m/s. Convert to km/hr: 25 × (18/5) = 90 km/hr. This matches option E.

Multiple choice

What is the length of the platform? I. Train X running at the speed of 25 km/hr crosses a platform in 18 seconds. II. Train X crosses a man moving at the speed of 5 km/hr in the opposite direction in 12 seconds. III. Train X crosses a pole in 14.4 seconds.

  1. Any two

  2. I and either II or III

  3. Any one

  4. Only III

  5. Only II
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

From I and II: Platform length = (25+5) × 5/18 × 12 = 100 m train length. Then from I: 100 + platform = 25 × 5/18 × 18 = 125, so platform = 25 m. From I and III: Train length = 25 × 5/18 × 14.4 = 100 m, same calculation. Either II or III gives train length when combined with I. III alone gives only train length (100 m), not platform. II alone is insufficient without train speed from context.

Multiple choice

The following questions are accompanied by three statements A, B and C. You have to determine which statement is/are sufficient. At what time will the train reach from city 'X' to city 'Y'? A. The train crosses another train of equal length of 200 meters and running in opposite direction in 30 seconds. B. The train leaves city 'Y' at 9.00 am for city 'X' situated at a distance of 780 kms. C. 250 meter long train crosses a signal pole in 10 seconds.

  1. Only A

  2. Only B

  3. Only C

  4. Only B and C

  5. All A, B, C are required to answer the question
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

From C: Train speed = 250 meters / 10 seconds = 25 m/s = 90 km/hr. From B: Distance = 780 km, departure = 9:00 am. Time = 780/90 = 8.67 hours = 8 hours 40 minutes. Arrival time can be calculated. Statement A about crossing another train is irrelevant. So only B and C are needed.

Multiple choice

A 300m long train moving with an average speed of 126 km/hr. crosses a platform in 24 seconds. A man crosses the same platform in 5 minutes .Find approx time required by train to cross the man?

  1. 8 sec

  2. 9 sec

  3. 23 sec

  4. 25 sec

  5. Cannot be determined
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

The problem is missing critical information: the man's position on the platform (where he starts or is located when the train begins crossing) and whether he is stationary or moving. Without knowing the relative positions of the train and man, the crossing time cannot be uniquely determined.

Multiple choice

What is the speed of the train? Statement I: The length of the train is 120 m. Statement II: The train crosses another 180 m long train in 4 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 gives only train length (120 m), insufficient without time. Statement II mentions crossing another 180 m train in 4 seconds, but lacks direction information (same or opposite direction) and speed of the other train. Combined, we still need the other train's speed or direction.

Multiple choice

The questions given below contain three statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question? What is the speed of a running train? I. The train crosses another train running in the opposite direction in 72 seconds. II. The length of the first train is 100 metres. III. The length of the second train is 180 metres.

  1. All are necessary

  2. All together are not sufficient

  3. Only II and III

  4. Only I and II

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

To find the speed of the first train, we need distance covered and time taken. When trains move in opposite directions, relative speed = sum of individual speeds. Distance = sum of lengths (100m + 180m = 280m), time = 72 seconds. So relative speed = 280/72 m/s. But we need the speed of the FIRST train specifically, not just relative speed. Without knowing the second train's speed, we cannot determine the first train's speed. The statements are insufficient.

Multiple choice

Two trains can cross a pole in 14 sec. and 16 sec. respectively. Find in how much time will they cross each other if they are coming from same direction and if the speed of the trains are in the ratio of 7 : 9. दो ट्रेनें एक खम्भे को क्रमशः 14 से. और 16 से. पर करती हैं | ज्ञात कीजिये कि कितने समय में वह एक दूसरे को पार कर लेंगी यदि वे एक ही दिशा से आ रही हैं और यदि ट्रेनों की गतियों का अनुपात 7 : 9 में है |

  1. 111 sec./से.

  2. 119 sec./से.

  3. 131 sec./से.

  4. 121 sec./से.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Train lengths from pole crossing: L₁ = 14 × 7k = 98k units, L₂ = 16 × 9k = 144k units. When moving in same direction, relative speed = 9k - 7k = 2k. Time to cross = (98k + 144k) / 2k = 121 sec.

Multiple choice

A train of length 280 m. long is moving with the speed of 108 km/hr. crosses a platform in 12 seconds. A man crosses this platform in 10 seconds. What is the speed of the man (in m./sec.) 108 किमी./घंटा की गति से चाल रही एक 280 मी. लम्बी ट्रेन 12 सेकेण्ड में एक प्लेटफ़ॉर्म पार करती है | एक आदमी इसी प्लेटफ़ॉर्म को 10 सेकेंड में पार करता है | इस आदमी की मीटर/सेकेंड गति क्या है ?

  1. 5 m./sec.(मी./से.)

  2. 8 m./sec.(मी./से.)

  3. 10 m./sec.(मी./से.)

  4. 12 m./sec.(मी./से.)
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Train speed = 108 km/hr = 30 m/s. Train + platform length = 30 × 12 = 360 m. So platform = 360 - 280 = 80 m. Man's speed = 80/10 = 8 m/s.

Multiple choice

A train having speed 48 km/hr. crosses another train running in opposite direction having the half of its length in 12 seconds. If the same train crosses a railway platform in 45 seconds, then what will be the length of the platform ? 48 किमी/घंटा की चाल से चलने वाली एक रेलगाड़ी, विपरीत दिशा आ रही अपने की आधी लम्बाई वाली दूसरी रेलगाड़ी को 42 किमी/घंटा की चाल से 12 सेकंड में पार करती है। यदि यही रेलगाड़ी एक रेलवे प्लेटफार्म को 45 सेकंड में पार करती है तो प्लेटफार्म की लम्बाई क्या होगी ?

  1. 300 m/मी.

  2. 350 m/मी.

  3. 400 m/मी

  4. 450 m/मी.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Convert speeds to m/s: 48 km/hr = 40/3 m/s and 42 km/hr = 35/3 m/s. When trains cross in opposite directions, their relative speed is the sum: 40/3 + 35/3 = 25 m/s. Distance covered in 12 seconds = 25 × 12 = 300 m, which equals the sum of both train lengths (L + L/2 = 1.5L). So 1.5L = 300 m, giving L = 200 m. For the platform crossing: distance = 200 + platform_length. Using 40/3 m/s and 45 seconds, we get 200 + platform_length = (40/3) × 45 = 600 m, so platform_length = 400 m.

Multiple choice

A train running at the speed of 20 m/sec crosses a pole in 24 seconds less than the time required to cross a platform whose length is thrice of that of the train at the same speed. What is the length of the train?

  1. 100

  2. 120

  3. 160

  4. 240

  5. 250
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When a train crosses a pole, distance traveled equals its length. When crossing a platform three times its length, total distance is 4× length. Time difference = (4L - L)/20 = 3L/20 seconds. Given this equals 24 seconds: 3L/20 = 24, so L = 160 meters.

Multiple choice

A moving train, 132 metres long, overtakes another train of 176 metres long, moving in the same direction in 0.168 minutes. If the second train is moving at 60 km/hr., at what speed is the first train moving ? एक गतिशील ट्रेन जोकि 132 मीटर लम्बी है, समान दिशा में गतिशील 176 मीटर लम्बी ट्रेन को 0.168 मिनट में पार करती है। यदि दूसरी ट्रेन 60 किमी/घंटा की रफ्तार से चल रही है तो पहली ट्रेन की चाल क्या है ?

  1. 170 km/hr किमी/घंटा

  2. 100 km/hr किमी/घंटा

  3. 110 km/hr किमी/घंटा

  4. 50 km/hr किमी/घंटा
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total distance to cover = 132 + 176 = 308 m = 0.308 km. Time = 0.168 min = 0.0028 hr. Relative speed = 0.308/0.0028 = 110 km/hr. First train speed = relative speed + second train speed = 110 + 60 = 170 km/hr.

Multiple choice

A train 150 metre long passes a standing man in 15 second. While it crosses another train of the same length coming from opposite direction in 12 seconds. Find the speed of the second train.

  1. 40 km/hr

  2. 45 km/hr

  3. 50 km/hr

  4. 54 km/hr
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

First train's speed = 150m/15s = 10 m/s. When trains cross in opposite directions, relative speed = sum of speeds. Total distance = 150 + 150 = 300m. Time = 12s, so relative speed = 300/12 = 25 m/s. Second train's speed = 25 - 10 = 15 m/s = 15 × (18/5) = 54 km/hr. The key is understanding relative speed in opposite directions.

Multiple choice

Two trains of lengths 108 m and 112 m are running in opposite direction (i.e. to each other). The speed of one of those trains is 45 km/hr. and the time taken by them to cross each other is 8 seconds. What is the speed of the other train?

  1. 50 km/hr.

  2. 54 km/hr.

  3. 60 km/hr.

  4. 64 km/hr.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When trains move in opposite directions, their relative speed is the sum of individual speeds. Total distance to cover = 108 + 112 = 220 m. Time taken = 8 seconds. Relative speed = 220/8 = 27.5 m/s = 27.5 × (18/5) = 99 km/hr. If one train's speed is 45 km/hr, the other train's speed = 99 - 45 = 54 km/hr.