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

Train A crosses a pole in 25 seconds and train B crosses the pole in 1 minute 15 seconds. Length of train A is half the length of train B. What is the ratio between the the speed of A and B respectively ? रेलगाड़ी A एक स्तम्भ को 25 से. में पार करती है और रेलगाड़ी B स्तम्भ को 1 मिनट 15 से. में पार करती है। रेलगाड़ी A की लंबाई रेलगाड़ी B की लंबाई की आधी है। । और B की चाल का क्रमशः अनुपात क्या है?

  1. 3 : 2

  2. 3 : 4

  3. 4 : 3

  4. 2 : 3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let length of train A = L, length of train B = 2L. Speed of A = L/25, Speed of B = 2L/75 = L/37.5. Ratio A:B = (L/25)/(L/37.5) = 37.5/25 = 3/2 = 3:2. Verify: If A=150m, B=300m, Speed A=6m/s, Speed B=4m/s, ratio=3:2.

Multiple choice

A train 240 m. long, travelling at 90 km./hr. overtake another train travelling in the same direction at 72 km./hr. and passes it completely in 80 seconds. The length of the second train in metres is - एक 240 मी. लम्बी ट्रेन 90 किमी./घं. की चाल चलते हुये उसी दिशा में दूसरी ट्रेन 72 किमी./घं. से चलते हुए को पूर्णतया 80 सेकेण्ड में पार करती है। तो दूसरी ट्रेन की लम्बाई (मीटर में) क्या है?

  1. 160

  2. 400

  3. 248

  4. 180
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Relative speed = 90 - 72 = 18 km/hr = 5 m/s. In 80 seconds, distance covered = 5 × 80 = 400m. This equals sum of both train lengths, so second train length = 400 - 240 = 160m.

Multiple choice

Two trains starting at the same time from two stations 200 km. apart and going in opposite direction cross each other at a distance of 110 km. from one of them. The ratio of their speeds is - दो ट्रेन एक ही समय पर 200 किमी. की दूरी पर दो स्टेशनों से विपरीत दिशा में चलना प्रारम्भ करती है। उनमें से एक से 110 किमी. की दूरी पर वे एक दूसरे को पार करती है तो उनकी चालों का अनुपात क्या है?

  1. 11 : 20

  2. 9 : 20

  3. 11 : 9

  4. 11 : 10
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total distance = 200 km. They cross at 110 km from one station, so one train traveled 110 km and the other traveled 200 - 110 = 90 km in the same time. Speed ratio = Distance ratio = 110:90 = 11:9. This works because when two objects start simultaneously and travel for equal durations, their speeds are directly proportional to distances covered.

Multiple choice

A 330 meter long toy train crosses another 110 meter long toy train coming from opposite direction in 55 seconds. If the speed of a toy train is 12 km./hr. What is the speed of second toy train? एक 330 मीटर लम्बी खिलौना ट्रेन विपरीत दिशा से आ रही 110 मीटर लम्बी दूसरी खिलौना ट्रेन को 55 सेकेण्ड में पार कर लेती है यदि एक खिलौना ट्रेन की चाल 12 किमी./घं. हो तो दूसरी खिलौना ट्रेन की चाल क्या होगी?

  1. 12.8 km./hr.

  2. 14 km./hr.

  3. 16 km./hr.

  4. 16.8 km./hr.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total distance covered = sum of train lengths = 330 + 110 = 440 m = 0.44 km. Time = 55 seconds = 55/3600 hours. Relative speed = Distance/Time = 0.44/(55/3600) = 28.8 km/hr. Since trains move in opposite directions, relative speed = sum of individual speeds: 12 + v = 28.8, giving v = 16.8 km/hr.

Multiple choice

A train passes through a tunnel whose length is 500 metres in 1 minute while running at a speed of 72 km per hour. The length of the train is- एक रेलगाड़ी 500 मी. लम्बी सुरंग को 72 किमी/घंटा की चाल से 1 मिनट में पार करती है। रेलगाड़ी की लम्बाई है-

  1. 750 m./मी.

  2. 700 m./मी.

  3. 800 m./मी.

  4. 680 m./मी.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Train speed = 72 km/h = 20 m/s. In 1 minute (60 seconds), distance covered = 20 × 60 = 1200 m. This distance equals tunnel length + train length. So train length = 1200 - 500 = 700 m. The train must completely exit the tunnel.

Multiple choice

Length of a express train is 215 metres which crosses another passenger train coming from opposite direction at 32 Km/h and 175 metre long in 18 second. Find the speed of express train. एक एक्सप्रेस ट्रेन की लंबाई 215 मीटर है जो एक दूसरी यात्री ट्रेन को जोकि विपरीत दिशा से 32 किमी /घंटा से आ रही है और 175 मीटर लम्बी है को 18 सेकंड में पार करती है। एक्सप्रेस ट्रेन की गति ज्ञात करें ।

  1. 42 km/h / किमी/घंटा

  2. 56 km/h / किमी/घंटा

  3. 46 km/h / किमी/घंटा

  4. 66 km/h / किमी/घंटा
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When two trains cross in opposite directions, their relative speed is the sum of their individual speeds. Total distance to cover = sum of train lengths = 215 + 175 = 390 metres. Time taken = 18 seconds. Relative speed = 390/18 = 21.67 m/s. Converting to km/h: 21.67 × (18/5) = 78 km/h. Since the passenger train moves at 32 km/h in opposite direction, express train speed = 78 - 32 = 46 km/h.

Multiple choice

A train crosses a pole in 15 seconds and crosses a platform of 150 metre length in 25 seconds. Find the speed of the train in Km/h.

  1. 40 Km/h

  2. 36 Km/h

  3. 50 Km/h

  4. 45 Km/h

  5. 54 Km/h
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

When the train crosses a pole in 15 seconds, it covers its own length L. When it crosses a 150m platform in 25 seconds, it covers L+150. The extra 10 seconds are for the 150m platform, so speed = 150÷10 = 15 m/s. Converting to km/h: 15 × 3.6 = 54 km/h. Options A (40), B (36), C (50), and D (45) are all incorrect conversions.

Multiple choice

Two trains are moving on two parallel tracks but in opposite directions. A person sitting in the first train moving at the speed of 80 km./hr. passes the second train in 18 seconds. If the length of the second train is 1000 m, its speed is- दो समांतर पथों पर लेकिन विपरीत दिशा में दो रेलगाड़ियां चल रही हैं। पहली ट्रेन में बैठा एक व्यक्ति जिसकी चाल 80 किमी./घण्टा है दूसरी ट्रेन को 18 सेकेण्ड में पार करती है। यदि दूसरी ट्रेन की लम्बाई 1000 मी. है, इसकी चाल है-

  1. 100 km.hr./किमी./घण्टा

  2. 120 km.hr./किमी./घण्टा

  3. 140 km.hr./किमी./घण्टा

  4. 150 km.hr./किमी./घण्टा
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. Distance covered = length of second train = 1000 m = 1 km. Time = 18 seconds = 18/3600 hours = 1/200 hours. Relative speed = Distance/Time = 1 ÷ (1/200) = 200 km/hr. Therefore, speed of second train = 200 - 80 = 120 km/hr.

Multiple choice

A train of length x m. passes a 300 m. long platform in 25 seconds at its usual speed. The train crosses a pole in 20 seconds at 50% of its usual speed. What is the value of x? अपनी सामान्य चाल से चलते हुए x मी. लम्बी एक ट्रेन 300 मी. लम्बे एक प्लेटफार्म को 25 सेकेण्ड में पार करती है। यह ट्रेन एक खम्भे को अपनी सामान्य चाल के 50% से चलकर 20 सेकेण्ड में पार करती है। तो x का मान क्या है?

  1. 160 m/मी.

  2. 260 m/मी.

  3. 200 m/मी.

  4. 310 m/मी.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let usual speed = v. At 50% speed (v/2), crossing pole takes 20s, so train length x = (v/2)*20 = 10v, giving v = x/10. At usual speed, crossing 300m platform takes 25s, so x+300 = v*25. Substituting v: x+300 = (x/10)*25, giving x+300 = 2.5x, so 300 = 1.5x, and x = 200m. The key insight is relating the two scenarios through the train's speed.

Multiple choice

A train 150 m long, passes a 150 m. long platform in 30 seconds and another train of the same length travelling in the opposite direction in 12 sec. The speed of the second train is 150 मी. लम्बी एक ट्रेन 150 मी. लम्बे एक एक प्लेटफार्म को 30 सेकेण्ड में पार करती है और विपरीत दिशा में चल रही समान लम्बाई की दूसरी ट्रेन को 12 सेकेंड में पार करती है | दूसरी ट्रेन की चाल है

  1. 45 km./hr.(किमी./घंटा)

  2. 48 km./hr.(किमी./घंटा)

  3. 52 km./hr.(किमी./घंटा)

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

Train speed: (150+150)/30 = 10 m/s = 36 km/h. Relative speed when crossing opposite train: (150+150)/12 = 25 m/s. If second train's speed is x, then 36+x = 25×3.6 = 90 km/h. So x = 54 km/h. The key is understanding relative speed concept and unit conversion from m/s to km/h.

Multiple choice

A train crosses a 50 meter platform in 14 seconds and crosses a man standing on the platform in 10 seconds. Find the speed of the train in km/h?

  1. 45

  2. 24

  3. 36

  4. 40
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Train crosses a man in 10 seconds, so train length = speed × 10. Train crosses 50m platform in 14 seconds, so train length + 50 = speed × 14. Solving: speed × 14 - speed × 10 = 50, so speed × 4 = 50, giving speed = 12.5 m/s. Converting to km/h: 12.5 × 18/5 = 45 km/h.

Multiple choice

A train travelling at 96 km/hr. crosses another train, having double its length and travelling in opposite direction at 84 km/hr. in 24 seconds. If train passes a railway platform in 45 seconds. The length of the platform is - 96 किमी./घं. की चाल से गति करती हुई एक ट्रेन स्वयं की लम्बाई की दुगुनी लम्बाई वाली दूसरी ट्रेन जोकि विपरीत दिशा में 84 किमी./घंटा की चाल से गति कर रही है, को 24 सेकेण्ड में पार करती है। यदि ट्रेन एक रेलवे प्लेटफार्म को 45 सेकेण्ड में पार करती है। प्लेटफार्म की लम्बाई है-

  1. 200 m./मी.

  2. 300 m./मी.

  3. 350 m./मी.

  4. 400 m./मी.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let first train length = L. Second train length = 2L. Relative speed = 96+84 = 180 kmph = 50 m/s. In 24 seconds, they cover L+2L = 3L, so 3L = 50×24 = 1200, giving L = 400m. Let platform length = P. Train covers L+P in 45 seconds at 96 kmph = 80/3 m/s. So 400+P = (80/3)×45 = 1200, giving P = 350m.

Multiple choice

A 280 meter long train moving with an average speed of 72 km/hr. crosses a platform in 23 seconds. A man crosses the same platform in 15 seconds. What is the speed of man in m/s. एक 280 मी. लंबी ट्रेन जोकि 72 किमी./घंटा की औसत चाल में चल रही है, एक प्लेटफार्म को 23 से. में पार करती है। एक व्यक्ति उसी प्लेटफार्म को 15 से. में पार करता है। आदमी की चाल मी./से. में क्या है?

  1. 8 m/s.

  2. 10 m/s.

  3. 12 m/s.

  4. 15 m/s
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Train speed = 72 km/h = 72×(5/18) = 20 m/s. Total distance in 23s = 20×23 = 460m. Platform length = 460 - 280 = 180m. Man's speed = 180/15 = 12 m/s. The problem has calculation inconsistency in the options - actual answer should be 12 m/s, which matches option C.

Multiple choice

A train travelling at a constant speed crosses a pole in 12 seconds whereas cross a tunnel 198 metre long in 30 seconds. Find the length of train. एक समान चाल से चलने वाली एक रेलगाड़ी एक खम्भे को 12 सेकेण्ड में पार करती है जबकि 198 मीटर लम्बी सुरंग को 30 सेकेण्ड में पार करती है। रेलगाड़ी की लम्बाई ज्ञात कीजिए।

  1. 132 metre/मीटर

  2. 143 metre/मीटर

  3. 165 metre/मीटर

  4. 150 metre/मीटर
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let train length = L meters and speed = v m/s. Crossing a pole: L = v × 12, so v = L/12. Crossing a 198m tunnel: L + 198 = v × 30. Substituting v: L + 198 = (L/12) × 30 = 2.5L. So 198 = 1.5L, giving L = 198/1.5 = 132 meters. Verification: Speed = 132/12 = 11 m/s. Time for tunnel = (132 + 198)/11 = 330/11 = 30 seconds, which matches.