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

Two trains are running at 40 km/hr. and 70 km/hr. respectively in the same direction. Fast train completely passes a man sitting in the slower train in 12 seconds. What is the length of the fast train? समान दिशाओ में चल रही दो ट्रेन जिनकी चाल क्रमशः 40 किमी/घंटे और 70 किमी/घंटा हैं । तेज गति वाली ट्रेन धीमी गति वाली ट्रेन में बैठे एक ब्यक्ति को 12 सेकेण्ड में पार करती है । तेज गति वाली ट्रेन की लम्बाई क्या है?

  1. 50 meter/मीटर

  2. 150 meter/मीटर

  3. 100 meter/मीटर

  4. 240 meter/मीटर
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When trains move in same direction, relative speed = 70 - 40 = 30 km/hr. Converting to m/s: 30 × (5/18) = 25/3 m/s. Distance covered in 12 seconds = (25/3) × 12 = 100 meters. This distance equals the length of the fast train.

Multiple choice

A train of length 175 m. takes 10 seconds to pass by another train 125 m. long coming from the opposite direction. If the speed of the first train be 30 km/hr. the speed of the second train (in km/hr.) is-

  1. 60

  2. 72

  3. 78

  4. 84
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total distance = 175 + 125 = 300 m covered in 10 seconds. Relative speed = 300/10 = 30 m/s. First train: 30 km/hr = 30 × 5/18 = 25/3 m/s. Second train speed: 30 - 25/3 = 65/3 m/s = 65/3 × 18/5 = 78 km/hr. Option C is correct.

Multiple choice

Two trains are running in opposite direction with speeds 36 and 54 km. per hour. If the trains be of length 132 metres and 118 metres respectively, they will cross each other in-

  1. 10 sec.

  2. 8 sec.

  3. 12 sec.

  4. 14 sec.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

When trains move in opposite directions, their relative speed is the sum: 36 + 54 = 90 km/h. Convert to m/s: 90 × (5/18) = 25 m/s. Total distance to cross = sum of lengths = 132 + 118 = 250 m. Time = Distance / Speed = 250/25 = 10 seconds. The 8 second option would be correct if trains were moving in the same direction.

Multiple choice

Two trains of lengths 120 m and 90 m are running with a speed of 80 km/h and 55 km/h respectively towards each other on parallel lines. If they are 90 m apart, after how many seconds they will cross each other?

  1. 5.6 second

  2. 7.2 second

  3. 8 second

  4. 9 second
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When trains move toward each other, add their speeds to get relative speed: 80 + 55 = 135 km/h = 135 × 5/18 = 37.5 m/s. Total distance to cross = sum of train lengths + initial gap = 120 + 90 + 90 = 300 m. Time = distance/speed = 300/37.5 = 8 seconds. Option A (5.6s) forgets to add train lengths; Option B (7.2s) uses wrong speed conversion; Option D (9s) miscalculates the distance.

Multiple choice

A train is 216 m long. It crosses a platform in 19 seconds with speed 21 m/s. If some 21 m long boxes are added in the train then it crosses the same platform in 27 seconds at the same speed. Then find the number of boxes that were added in the train.

  1. 2

  2. 6

  3. 12

  4. 8

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

Distance to cross platform = Train length + Platform length. At 21 m/s for 19 seconds, total distance = 21 × 19 = 399 m. Platform length = 399 - 216 = 183 m. After adding n boxes of 21 m each, new train length = 216 + 21n. Total distance = (216 + 21n) + 183 = 399 + 21n. At same speed for 27 seconds: 21 × 27 = 567 = 399 + 21n. Therefore 21n = 168 and n = 8 boxes.

Multiple choice

Two trains of length 1100 meters and 900 meter are running on parallel lines in the same direction with a speed of 35 km/hr. and 40 km/hr. respectively. In what time will they pass each other? 1100 मीटर और 900 मीटर की लंबाई वाली दो ट्रेनें समान दिशा में क्रमशः 35 किमी / घंटा और 40 किमी / घंटा की गति से समान दिशा में चल रही हैं। । किस समय में वे एक दूसरे को पार करेंगी?

  1. 36 minutes/मिनट

  2. 30 minutes/मिनट

  3. 28 minutes/मिनट

  4. 24 minutes/मिनट
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

When trains move in the same direction, relative speed is the difference of their speeds: 40 - 35 = 5 km/hr = 25/18 m/s. The total distance to cover is the sum of both train lengths: 1100 + 900 = 2000 m. Time = Distance/Relative Speed = 2000/(25/18) = 1440 seconds = 24 minutes. The distractor of 36 minutes would result from incorrectly adding the speeds instead of subtracting.

Multiple choice

Two trains of lengths 300 m and 360 m respectively are running in opposite directions on the parallel tracks. If their speeds be 100 km/hr and 116 km/hr respectively, in what time will they cross each other? दो रेलगाड़ियाँ जिनकी लम्बाईयाँ क्रमशः 300 मी और 360 मी है, समान्तर पथों पर एक दूसरे के विपरीत दिशा में दौड़ रहीं हैं | यदि उनकी गतियाँ क्रमशः 100 किमी./घंटा और 116 किमी./घंटा हैं |तो कितने समय में वे एक दूसरे को पार कर लेंगीं ?

  1. 12 seconds/ सेकेण्ड

  2. 15 seconds/ सेकेण्ड

  3. 13 seconds/ सेकेण्ड

  4. 11 seconds/ सेकेण्ड
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total distance = 300 + 360 = 660 m. Relative speed when opposite = 100 + 116 = 216 km/hr = 216×(5/18) = 60 m/s. Time = 660/60 = 11 seconds. Options A, B, C are arithmetic errors in unit conversion or calculation.

Multiple choice

A train which is 595 m long can cross a pole in 17 seconds. If it halts 5 times each time for exactly 8 minutes, how many time will it take to cover a distance of 1197 kms?

  1. 9 hr 30 min

  2. 10 hr 30 min

  3. 10 hr 10 min

  4. 10 hr 40 min

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

Speed = distance/time = 595m/17s = 35 m/s. Distance = 1197 km = 1,197,000 m. Travel time = 1,197,000/35 = 34,200 seconds = 570 minutes = 9 hours 30 minutes. Halts = 5 × 8 = 40 minutes. Total = 9h 30min + 40min = 10h 10min. This matches option C.

Multiple choice

How many seconds will a 120 metres long train running at the rate of 36 km/hr take to cross a bridge of 360 metres in length? 36 किमी/घंटा की गति से चल रही 120 मीटर लम्बी रेलगाड़ी 360 मीटर लंबे पुल को पार करने में कितने सेकेंड लेगी?

  1. 48 seconds/सेकेंड

  2. 36 seconds/सेकेंड

  3. 40 seconds/सेकेंड

  4. 46 seconds/सेकेंड
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total distance = train length + bridge length = 120 + 360 = 480 m. Speed = 36 km/h = 36×5/18 = 10 m/s. Time = 480/10 = 48 seconds.

Multiple choice

After how many time train A and train B meet to each other. Statement I: Train A from point P and train B from point Q started travelling towards each other at 6:00am and 7:30 am respectively and reaches their destination point Q at 12:20pm and point P at 03:06pm resp. Statement II: Speed of train A is 10km/h more than speed of train B. Statement III: length of train A is 100m more than length of train B.

  1. I and either II or III

  2. I and II

  3. III and either I or II

  4. II and III

  5. only I
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

From Statement I: Train A travels from 6:00 AM to 12:20 PM (6h 20m = 19/3 hours). Train B travels from 7:30 AM to 3:06 PM (7h 36m = 19/3 hours). Both take the same time, so if speeds are v_A and v_B with distance d, then d/v_A = d/v_B, meaning v_A = v_B. When both move toward each other starting at 7:30 AM, relative speed = 2v and they meet when combined distance = d, which happens at time t such that 2vt = d. Since d = v × 19/3, meeting time = 19/6 hours after 7:30 AM. Statement I alone is sufficient.

Multiple choice

Which information are necessary to answer the questions asked- What is the length of the train? Statement I: If train can cross a platform in 35 second and a pole in 15 sec. Statement II: If the speed of train is 70 kmph. Statement III: If the length of platform is 400 m.

  1. I and (II or III) together

  2. I alone

  3. I and II together

  4. II and III together

  5. Even all I, II, and III are not sufficient
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

From Statement I: Crossing pole in 15 sec gives L = 15v, and crossing platform in 35 sec gives L + p = 35v. This alone is insufficient (2 equations, 3 unknowns). With Statement II (speed = 70 kmph): convert to m/s, use L = 15v to find length. With Statement III (p = 400 m): substitute into L + 400 = 35v and L = 15v, solve to get L = 300 m. Thus I + (II or III) is sufficient.

Multiple choice

Find the speed of the train whose length is 270m? Statement I: A train 270 meter long, passes a bird flying in a straight line at the speed of 9 kmph in the opposite direction in which the train is going, in 12 seconds. Statement II: The train passes another train of length 230 m in 10 sec. Statement III: The speed of the second train is 30m/s.

  1. Any two

  2. I and II

  3. I and II or III

  4. Only I

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

Statement I alone is sufficient: train length 270m, bird speed 9 kmph (2.5 m/s) opposite direction, time 12 sec. Relative speed = 270/12 = 22.5 m/s. Since opposite direction, train speed = 22.5 - 2.5 = 20 m/s = 72 km/h. Statement II requires unknown direction/speed of other train. Statement III only gives second train's speed without context about first train.

Multiple choice

The length of Rajdhani train and Passenger train are 200 m and 150 m respectively. They cross each other in 18 seconds. Then find the speed of Passenger train in km/hrs., if the speed of Rajdhani train is 25 km/hrs.

  1. 40 km/hrs.

  2. 30 km/hrs.

  3. 45 km/hrs.

  4. 55 km/hrs.

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

Relative speed = (200 + 150)/18 = 350/18 m/s. Rajdhani speed = 25 km/hr = 25×5/18 = 125/18 m/s. Let passenger train speed = v. Then 125/18 + v = 350/18. Solving: v = 225/18 m/s = 225/18 × 18/5 = 45 km/hr.