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 man crosses a stationary train in 15 minutes. The same train crosses a man in 50 seconds. What is the respective ratio between the speed of the train and the man ?

  1. Can’t be determined

  2. 1 : 16

  3. 18 : 1

  4. 12 : 7
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

When a man crosses a stationary train, his distance covered equals the train's length. When the train crosses a stationary man, the train covers its own length. Both scenarios give train length = speed_man × 15 min = speed_train × 50 sec. This gives speed_train/speed_man = (15 × 60)/50 = 18, BUT this assumes man's speed is constant across both scenarios, which is not necessarily true. Without this assumption, the ratio is undetermined.

Multiple choice

Two trains start simultaneously from A and B 180 kms apart, towards B and A respectively at speeds in the ratio 5 : 4. They cross each other at M and after reaching B and A turn back immediately and meet again at N. Find the distance MN.

  1. 45 km.

  2. 40 km.

  3. 35 km.

  4. 42 km.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let speeds be 5x and 4x. First meeting at M: distances covered are in ratio 5:4, so train from A travels (5/9)×180 = 100 km to reach M. Second meeting at N: after first meeting, trains continue to destinations (train from A travels 80 km more to B, train from B travels 100 km more to A), then turn back. Total distance covered by both trains between first and second meeting is 2×180 = 360 km. Train from A covers (5/9)×360 = 200 km in this period. But from M to B is 80 km, and B to A is 180 km, so from M, it goes 80 + 180 = 260 km to reach A, but it only covers 200 km total. So from M towards A after the turn, it covers 200 - 80 = 120 km. Distance from A = 180 - 120 = 60 km. M was at 100 km from A, so MN = 100 - 60 = 40 km. Alternatively, using the formula: For two trains starting from opposite ends, MN = (difference in speeds)/(sum of speeds) × distance between starting points = (5x-4x)/(5x+4x) × 180 = (1/9) × 180 = 20 km from one end. But M is at 100 km from A, so N is at 100 - 40 = 60 km from A, giving MN = 40 km.

Multiple choice

Two trains 108 m and 112 m in length are running towards each other on parallel lines at a speed of 45 km/hr. and 54 kmph respectively. How long will it take them to cross each other after they meet ?

  1. 6 sec

  2. 8 sec

  3. 7 sec

  4. 10 sec
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Trains are running towards each other, so relative speed = 45 + 54 = 99 km/hr = 99 × (5/18) = 27.5 m/s. Total distance to cover = sum of lengths = 108 + 112 = 220 m. Time = Distance/Speed = 220/27.5 = 8 seconds. Option A (6 sec), C (7 sec), and D (10 sec) are incorrect. The key is understanding that 'after they meet' means the time to completely cross each other, which uses relative speed and total length.

Multiple choice

Two trains 100 meters and 95 meters long respectively pass each other in 27 seconds when they run in the same direction and in 9 seconds when they run in opposite directions. Speed of the two trains are

  1. 44km/hr : 22 km/hr

  2. 52km / hr : 26 km / hr

  3. 36 km / hr : 18 km/hr

  4. 40 km / hr : 20 lm / hr
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let speeds be v1 and v2 km/hr (v1 > v2 for same direction case). Same direction: relative speed = v1 - v2 = (100+95)/27 km/sec = 195/27 × 18/5 = 26 km/hr. Opposite direction: relative speed = v1 + v2 = (100+95)/9 km/sec = 195/9 × 18/5 = 78 km/hr. Solving v1 - v2 = 26 and v1 + v2 = 78 gives v1 = 52 km/hr and v2 = 26 km/hr. Therefore option B is correct.

Multiple choice

A train passes a man standing on a platform in 8 seconds and also crosses the platform which is 264 metres long in 20 seconds. The length (in meters) of the train is

  1. 188

  2. 176

  3. 175

  4. 96
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When the train passes a man, it covers its own length in 8 seconds at speed v, so length L = 8v. When it crosses a 264m platform in 20 seconds, it covers L + 264 = 20v. Substituting L = 8v gives 8v + 264 = 20v, so 12v = 264 and v = 22 m/s. Therefore L = 8 x 22 = 176 meters.

Multiple choice

A train is moving at a speed of 132 km/hr. If the length of the train is110 metres, how long will it take to cross a railway platform 165 metres long? एक ट्रेन 132 किमी / घंटे की चाल से चल रही है। यदि ट्रेन की लम्बाई 110 मीटर हो तो यह 165 मीटर लम्बे एक रेलवे प्लेटफार्म पार करने के लिए कितना समय लेगी?

  1. 7 ½ sec

  2. 8 ½ sec

  3. 9 ½ sec

  4. 11 ½ sec

  5. 12 ½ sec
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To cross a platform, the train must travel its own length plus the platform length. Total distance = 110 + 165 = 275 m. Speed in m/s = 132 × (5/18) = 36.67 m/s. Time = 275/36.67 ≈ 7.5 seconds.

Multiple choice

A superfast train whose length is 280 meters crosses a tunnel in 27 seconds. If its speed is 60 Km/h then find the length of tunnel. एक ट्रेन जिसका लम्बाई 280 मीटर है एक सुरंग को 27 सेकंड में पार करती है। यदि ट्रेन की गति 60 किमी / घंटा है तो सुरंग की लम्बाई ज्ञात करें ।V

  1. 150 meter 150 मीटर

  2. 175 meter 175 मीटरV

  3. 225 meter 225 मीटर

  4. 170 meter 170 मीटर

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

Train speed = 60 kmph = 60 × 5/18 = 50/3 m/s. In 27 seconds, total distance covered = 27 × 50/3 = 450 meters. This distance equals train length + tunnel length = 280 + tunnel. Therefore tunnel = 450 - 280 = 170 meters. Remember to convert units consistently.

Multiple choice

What is the respective ratio between times taken by a train 320m. long to cross a electric pole and a bridge of 75 m. long? 320 मी. लम्बी एक ट्रेन द्वारा इलेक्ट्रिक पोल और 75 मी. लम्बे पुल को पार करने में लिये गये समयों के बीच क्रमशः क्या अनुपात है?

  1. 60 : 79

  2. 64 : 79

  3. 64 : 69

  4. 21 : 39

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

Time to cross pole = 320/v (train covers its own length). Time to cross bridge = (320+75)/v = 395/v (train covers its length plus bridge). Ratio = (320/v) : (395/v) = 320 : 395 = 64 : 79 after dividing by 5. Option B matches.

Multiple choice

Speed of a train is 44 Km/h and its length is 322 metre. It crosses another train coming from opposite direction at 28 Km/h in 25 seconds. Find the length of second train. एक ट्रेन की गति 44 किलोमीटर / घंटा है और इसकी लंबाई 322 मीटर है यह 28 किलोमीटर/ घंटा की गति से विपरीत दिशा से आने वाली एक दूसरी ट्रेन को 25 सेकंड में पार करती है। दूसरी ट्रेन की लंबाई ज्ञात करें।

  1. 125 metre 125 मीटर

  2. 178 metre 178 मीटर

  3. 240 metre 240 मीटर

  4. 210 metre 210 मीटर

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

When trains cross in opposite directions, their relative speed is the sum of individual speeds. Relative speed = 44 + 28 = 72 km/h = 72 × 5/18 = 20 m/s. Total distance covered in 25 seconds = 20 × 25 = 500 meters. This distance equals the sum of both train lengths. First train length = 322m. Second train length = 500 - 322 = 178m. The second train is 178 meters long.

Multiple choice

A 450 m long passenger train passes a goods train 300 m long travelling in opposite direction. If the speeds of the passenger train and goods train be 117 km/hr. and 63 km/hr., how long will it take to cross each other? एक 450 मीटर लम्बी यात्री ट्रेन 300 मीटर लम्बी मालगाड़ी विपरीत दिशाओं में यात्रा करती है। यदि यात्री ट्रेन और मालगाड़ी की गति 117 किमी / घंटा और 63 किमी / घंटा हो। एक दूसरे को पार करने में कितना समय लगेगा?

  1. 15 seconds 15 सेकेण्ड

  2. 30 seconds 30 सेकेण्ड

  3. 45 seconds 45 सेकेण्ड

  4. 60 seconds 60 सेकेण्ड

  5. 75 seconds 75 सेकेण्ड
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total distance = 450 + 300 = 750m. Relative speed (opposite directions) = 117 + 63 = 180 km/hr = 180 × (1000/3600) = 50 m/sec. Time = Distance / Speed = 750 / 50 = 15 seconds. The trains completely cross each other when the combined length has passed.

Multiple choice

Find the time taken by a train 265 meter long, running at a speed of 43.2 km/h to cross a river bridge 251 meter long. (in seconds) 265 मीटर लंबी ट्रेन जोकि 43.2 किमी / घंटा की गति से चल रही है, द्वारा 251 मीटर लंबे नदी के पुल को पार करने में लगा समय ज्ञात कीजिये । (सेकंड में)

  1. 35सेकंड

  2. 38सेकंड

  3. 41सेकंड

  4. 43सेकंड

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

Total distance = train length + bridge length = 265 + 251 = 516 m. Speed = 43.2 km/h = 43.2 * (1000/3600) = 12 m/s. Time = 516/12 = 43 seconds.

Multiple choice

The speed of two trains are in the ratio of 6:5. They are running in opposite direction on parallel tracks. If each takes 2 seconds to cross a pole. How many time they will take to cross each other? दो रेलगाड़ियों की चाल का अनुपात 6 : 5 है। वे विपरीत दिशा में अलग-अलग पटरियों पर दौड़ रही है। यदि प्रत्येक रेलगाड़ी खम्भे को पार करने में 2 सेकेण्ड का समय लेती है। एक दूसरे को पार करने में कितना समय लेगी?

  1. 4 seconds 4 सेकेण्ड

  2. 6 seconds 6 सेकेण्ड

  3. 2 seconds 2 सेकेण्ड

  4. 5 seconds 5 सेकेण्ड

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

Let speeds be 6x and 5x. Each train crosses a pole in 2 seconds, meaning length = speed × time. For first train: L1 = 6x × 2 = 12x. For second train: L2 = 5x × 2 = 10x. When crossing each other (opposite direction), relative speed = 6x + 5x = 11x. Total distance to cover = L1 + L2 = 12x + 10x = 22x. Time = Distance / Relative Speed = 22x / 11x = 2 seconds. The claimed answer C (2 seconds) is correct.

Multiple choice

A 130 m. long train running at the speed of 45 km./hr. crosses a bridge in 30 seconds. What is the length of the bridge? एक 130 मी. लम्बी रेलगाड़ी 45 किमी./घं की चाल से चलते हुए एक पुल को 30 सेकेण्ड में पार करती है। पुल की लम्बाई क्या है?

  1. 200 m.

  2. 225 m.

  3. 245 m.

  4. 250 m.

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

Convert speed: 45 km/hr = 45 × (1000/3600) = 12.5 m/s. Distance covered in 30s = 12.5 × 30 = 375 m. This equals train length + bridge length, so bridge = 375 - 130 = 245 m.