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 passes two bridges of length 400 m and 200 m in 50 seconds and 30 seconds respectively. The length of the train is एक ट्रेन दो पुलों जिनकी लम्बाईयाँ 400 मी. और 200 मी. हैं. को 50 से. और 30 से. में पार करती हैं | ट्रेन की लम्बाई है

  1. 40 m./मी.

  2. 45 m./मी.

  3. 75 m./मी.

  4. 100 m./मी.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

When a train passes a bridge, the distance covered equals the train's length plus the bridge's length. Using the two equations: (L + 400)/v = 50 and (L + 200)/v = 30, we divide them to eliminate speed and solve for L. This gives L = 100 meters. The speed works out to 10 m/s in both cases, confirming the answer.

Multiple choice

A 180 metres long train takes 90 seconds to cross a platform thrice its length. In what time will it take to cross a bridge whose length is 3/4th of the length of platform ?

  1. 73.125 sec

  2. 83 sec

  3. 76.25 sec

  4. 40 sec

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

Train length = 180 m. Platform length = 3 × 180 = 540 m. Total distance to cross platform = 180 + 540 = 720 m. Time = 90 seconds. Speed = 720/90 = 8 m/s. Bridge length = (3/4) × 540 = 405 m. Distance to cross bridge = 180 + 405 = 585 m. Time = 585/8 = 73.125 seconds.

Multiple choice

One train crosses a pole and a paltform in 18 seconds and 39 seconds respetively. The lenght of platform is 157.5 metre. What will be the length of another train whose length is equal to the sum of half of the length of first train and twice the length of the platform? एक ट्रेन एक खम्भे और एक प्लेटफार्म को क्रमशः 18 सेकेण्ड और 39 सेकेण्ड में पार करती है। प्लेटफार्म की लम्बाई 157.5 मी. है। दूसरी ट्रेन की लम्बाई क्या होगी जिसकी लम्बाई पहली ट्रेन की लम्बाई की आधी है एवं प्लेटफार्म की लम्बाई के दोगुने के योग के बराबर है?

  1. 238.5 m./ मी.

  2. 375 m./ मी.

  3. 328.5 m./ मी.

  4. 382.5 m./ मी.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let train length be L meters and speed be S m/s. Crossing a pole: L = 18S. Crossing platform: L + 157.5 = 39S. Substituting L = 18S: 18S + 157.5 = 39S, so 21S = 157.5, giving S = 7.5 m/s and L = 135 m. Second train length = (135/2) + (2 × 157.5) = 67.5 + 315 = 382.5 m.

Multiple choice

Two trains of equal length are running on parallel lines in the same direction at the rate of 46 km/hr. and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train in meter is- दो ट्रेन समान लम्बाई की एक ही दिशा में क्रमश: 46 किमी /घंटा और 36 किमी/घंटा की चाल से चल रही है यदि तेज गति वाली ट्रेन धीमी गति वाली ट्रेन को 36 सेकंड में पार करती है तो प्रत्येक ट्रेन की लम्बाई मी. में ज्ञात कीजिये|

  1. 45

  2. 54

  3. 50

  4. 65
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When trains move in the same direction, their relative speed is the difference of their speeds: 46 - 36 = 10 km/h = 25/9 m/s. To completely pass the slower train, the faster train must cover the sum of both lengths (2L). Using distance = speed × time: 2L = (25/9) × 36 = 100 m. Therefore, each train is 50 m long. Option A (45 m) and B (54 m) are incorrect calculations. Option D (65 m) would require different speeds or time.

Multiple choice

A train running at the speed of 20 metres/second crosses a pole in 24 seconds less than the time it requires to cross a platform thrice its length at the same speed. What is the length of the train? एक रेलगाड़ी जिसकी गति 20 मी./से. है, एक खम्भे को अपने से तीन गुने लम्बाई के प्लेटफार्म को पार करने में उसी गति से लगे समय से 24 सेकंड कम समय में पार करती है। रेलगाड़ी की लम्बाई क्या है?

  1. 270 metres/मीटर

  2. 340 metres/मीटर

  3. 180 metres/मीटर

  4. 160 metres/मीटर
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let train length be L. Time to cross pole = L/20 seconds. Time to cross platform = (L + 3L)/20 = 4L/20 = L/5 seconds. The difference: L/5 - L/20 = 24. Solving: (4L - L)/20 = 24, so 3L = 480, giving L = 160 metres. This is a standard train problem where crossing a pole requires covering the train's length, while crossing a platform requires covering train length plus platform length.

Multiple choice

A train crosses a platform in 30 seconds travelling with a speed of 60 km/h. If the length of the train be 400 metres, then the length (in metres) of the platform is एक रेलगाड़ी एक 60 किमी./घंटा की गति से एक प्लेटफार्म को 30 सेकण्ड्स में पार करती है | यदि रेलगाड़ी की लम्बाई 400 मीटर है, तो प्लेटफार्म की लम्बाई (मीटर में) है |

  1. 800

  2. 600

  3. 400

  4. 100
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Speed = 60 km/h = 60 × 1000/3600 = 50/3 m/s. Time taken to cross platform = 30 seconds. Total distance covered = length of train + length of platform = Speed × Time = (50/3) × 30 = 500 meters. Given train length = 400m, so platform length = 500 - 400 = 100 meters. The key is understanding that 'crossing the platform' means covering the train's own length plus the platform's length, and converting units consistently (km/h to m/s).

Multiple choice

A 250 m train is running at the average speed 90 km/hr. how long will it take to pass a standing man? एक 250 मी. लम्बी रेलगाड़ी 90 किमी प्रति घण्टे की औसत चाल से चल रही है। एक खड़े हुए आदमी को पार करने में उसे कितना समय लगेगा?

  1. 12.5 sec./से.

  2. 10 sec./से.

  3. 8 sec./से.

  4. 20 sec./से.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Distance = length of train = 250 m. Speed = 90 km/hr = 90 × (5/18) = 25 m/s. Time = Distance/Speed = 250/25 = 10 seconds. To pass a standing man, the train must cover its own length. Therefore, option B is correct.

Multiple choice

A train crosses a platform which is two times of the length of train in 18 sec. In how much time it can cross a pole? कोई रेलगाड़ी अपने से दो गुने लंबे प्लेटफार्म को 18 सेकेण्ड में पार करती है तो यह एक खम्भे को पार करने में कितना समय लेगी?

  1. 15 sec./से.

  2. 6 sec./से.

  3. 9 sec./से.

  4. 18 sec./से.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let train length be L. Platform length = 2L. Total distance to cross platform = L + 2L = 3L in 18 sec. Speed = 3L/18 = L/6 per sec. To cross pole (distance = L): time = L / (L/6) = 6 sec. Options A, C, D are incorrect.

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? एक 125 मी. लम्बी ट्रेन, 82 किमी./घं. की चाल से चल रही है, तो कितने समय में 8 किमी./घं. की चाल से विपरित दिशा से आ रहे लड़के को पार करेगी?

  1. 8 sec. / से.

  2. 9 sec. / से.

  3. 5 sec. / से.

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

Train speed = 82 km/hr, boy speed = 8 km/hr opposite direction. Relative speed = 82 + 8 = 90 km/hr = 90×(5/18) = 25 m/s. Time to cross = length/relative speed = 125/25 = 5 seconds.

Multiple choice

The numericle value of the speed of a train in km/hr is double of the time taken by it to cross a platform while it crosses a platform in 30 seconds. If the length of the train be 200 metres, then the length ( in metres) of the platform is एक ट्रेन की चाल का आंकिक मान किमी/घंण्टा में उस समय का दों गुना है जो एक प्लेटफार्म को पार करने में लगता है। जबकि यह प्लेटफार्म को 30 सेकेण्ड में पार करती है | यदि ट्रेन की लम्बाई 200 मीटर है, तो प्लेटफार्म की लम्बाई (मी. में) है -

  1. 400

  2. 300

  3. 200

  4. 500
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let time taken to cross platform = t seconds. Speed = 2t km/hr = (2t × 5/18) m/s. Distance to cross platform = train length + platform length = 200 + L. Time = distance/speed, so 30 = (200 + L) / (2t × 5/18). But t = 30 seconds (given), so speed = 60 km/hr = 60 × 5/18 = 50/3 m/s. Distance = speed × time = (50/3) × 30 = 500m. So L = 500 - 200 = 300m. The key insight is that the numeric value of speed in km/hr equals the time in seconds.

Multiple choice

Two trains running in opposite directions cross a man standing on the platform in 32 seconds and 20 seconds respectively and they cross each other in 42 seconds. The ratio of their speed is- दो रेलगाड़ी विपरीत दिशा में चल रही है, प्लेटफार्म पर खड़े एक व्यक्ति को क्रमशः 32 सेकेण्ड और 20 में पार करती है और वे एक दूसरे को 42 सेकेण्ड में पार करती है। उनकी चालों का अनुपात है -

  1. 13 : 7

  2. 9 : 7

  3. 13 : 11

  4. 11 : 5
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let train lengths be L1 and L2, speeds be S1 and S2. A man standing still is crossed when the train passes its own length. So L1/S1 = 32 and L2/S2 = 20. Thus L1 = 32S1 and L2 = 20S2. When trains cross each other (opposite direction), relative speed is S1 + S2. Time = (L1 + L2)/(S1 + S2) = 42. Substituting: (32S1 + 20S2)/(S1 + S2) = 42. Solving: 32S1 + 20S2 = 42S1 + 42S2, giving 20S2 - 42S2 = 42S1 - 32S1, or -22S2 = 10S1, so S1/S2 = -22/10 = -11/5. Since speed is positive, S1:S2 = 11:5. The ratio is 11:5.

Multiple choice

A train crosses a telegraph post in 8 sec. and a 200 m. long bridge in 24 sec. What is the length of the train? एक रेलगाड़ी एक संकेतक स्तम्भ को 8 सेकण्ड में और 200 मी. लम्बे पुल को 24 सेकण्ड में पार करती है । रेलगाड़ी की लम्बाई क्या है?

  1. 100 m/मी.

  2. 120 m/मी.

  3. 140 m/मी.

  4. 160 m/मी.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let train length = L and speed = v. Crossing a post: L = 8v. Crossing bridge: L + 200 = 24v. Substituting v = L/8 gives L + 200 = 3L, so 2L = 200 and L = 100m. The train travels its own length in 8 seconds.

Multiple choice

A 330 meter long train crosses an other 150 meter long train in 55 seconds. If the speed of a train is 24 km./hr. What is the speed of second train? एक 330 मीटर लम्बी ट्रेन 150 मीटर लम्बी दूसरीट्रेन को 55 सेकेण्ड में पार कर लेती है यदि एक ट्रेन की चाल 24 किमी./घं. हो तो दूसरी ट्रेन की चाल क्या होगी?

  1. 12 km./hr./किमी./घं.

  2. 24 km./hr./किमी./घं.

  3. 36 km./hr./किमी./घं.

  4. Data inadequate/डाटा अपर्याप्त
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The question states 'the speed of a train is 24 km/hr' but doesn't specify which train. Without knowing which train has this speed and whether they're moving in same or opposite directions, the second train's speed cannot be uniquely determined from given information.

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. दो ट्रेनें एकसाथ A और B जोकि 180 किमी. की दूरी पर स्थित हैं, से B और A की तरफ 5 : 4 की गतियों के अनुपात में चलती हैं | वे एक दूसरे को M पर मिलती हैं और B और A पर पहुंचकर तुरंत वापस आकर पुनः N पर मिलती हैं | MN की दूरी ज्ञात कीजिये |

  1. 45 km./किमी.

  2. 40 km./किमी.

  3. 35 km./किमी.

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

Trains meet first at M after covering 180 km together. Speeds 5x and 4x, so distances are 100 km and 80 km respectively. Total distance for second meeting is 3×180 = 540 km (each reaches destination and turns back). Distance MN = (540/9) × 2 = 40 km. Option A incorrectly uses the first meeting distance.

Multiple choice

A person standing on a railway platform noticed that a train takes 18 seconds to cross the platform of length 72 m. and it takes 12 seconds to cross him. Find the speed of the train (in km/hr.)? एक प्लेटफार्म पर खड़ा हुआ एक व्यक्ति यह ध्यान देता है कि एक ट्रेन 72 मी. लम्बाई के प्लेटफार्म को 18 सेकेण्ड में एवं उसे 12 सेकेण्ड में पार करती है। ट्रेन की चाल ज्ञात कीजिए। (किमी./घंटा)

  1. 42.3

  2. 43.2

  3. 46.5

  4. 45.6
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let train length = L and speed = v. Crossing platform: (L+72)/v = 18. Crossing person: L/v = 12, so L = 12v. Substituting: (12v+72)/v = 18 → 12v+72 = 18v → 6v = 72 → v = 12 m/s. In km/hr: 12 × (18/5) = 43.2 km/hr.