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

The ratio of speeds of a goods train and passenger train is 11:13 in the same direction. If the passenger train crosses the goods train in 90 seconds, while a passenger in the passenger train observes that he crosses the goods train in 75 seconds. Find the ratio of length of goods train to passenger train?

  1. 6 : 7

  2. 4 : 9

  3. 5 : 1

  4. 8 : 11

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

Let lengths be Lg and Lp. Speeds in ratio 11:13, so relative speed = 13-11 = 2 units. From outside, passenger train crosses goods train in 90s: (Lg + Lp)/2 = 90, so Lg + Lp = 180. From inside passenger train, only goods train's length passes: Lg/2 = 75, so Lg = 150. Then Lp = 180 - 150 = 30. Ratio Lg:Lp = 150:30 = 5:1. The key is recognizing that from inside, only the other train's length matters.

Multiple choice

There are two trains of same lengths one take 20 seconds and 30 seconds respectively to cross a telegraph post. Trains are travelling in opposite direction if the length of each train be 150 metres. In what time (in seconds) will they cross each other? एक ही लंबाई की दो ट्रेनें एक टेलीग्राफ पोस्ट को पार करने के लिए क्रमश: 20 सेकंड और 30 सेकंड का समय लेती हैं। यदि ट्रेन प्रत्येक ट्रेन की लंबाई 150 मीटर हो और ट्रेन विपरीत दिशा में चल रही है तो वे कितने समय (सेकंड में) एक दूसरे को पार करेंगी?

  1. 30 sec./सेकंड

  2. 24 sec./सेकंड

  3. 40 sec./सेकंड

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

Train speeds are 7.5 m/s (150/20) and 5 m/s (150/30) from telegraph post times. When moving in opposite directions, relative speed is 12.5 m/s. Total crossing distance is 300 m (sum of both lengths), so time = 300/12.5 = 24 seconds. The key is adding speeds for opposite direction motion.

Multiple choice

It takes 24 seconds for a train travelling at 93 kmph to cross entirely another train half its length travelling in opposite direction at 51 kmph. It passes a bridge in 66 seconds. What is the length of the bridge? (In m)

  1. 1065

  2. 1600

  3. 1705

  4. 1580

  5. 1000
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let length of first train = L. Then second train length = L/2. Relative speed = 93+51 = 144 kmph = 144×(5/18) = 40 m/s. Total distance covered in 24s = L + L/2 = 3L/2 = 24×40 = 960m. So L = 960×2/3 = 640m. Train passes bridge in 66s, so bridge length = (distance covered) - (train length) = 66×(93×5/18) - 640 = 66×25.92 - 640 = 1710.72 - 640 = 1070.72 ≈ 1065m (accounting for rounding in intermediate steps). Using exact fractions: speed = 93×5/18 = 155/6 m/s, bridge length = 66×155/6 - 640 = 11×155 - 640 = 1705 - 640 = 1065m.

Multiple choice

Find the value of quantities and state the correct relationship.\newline Quantity I: The length of the train if train crosses a pole in 30 sec and a platform of 300 m length in 60 seconds.\newline Quantity II: The length of a platform if 200 m long train crosses a pole in 25 sec and platform in 55 sec

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: Train speed = v. Crossing pole (length L) in 30s: v = L/30. Crossing 300m platform in 60s: (L+300)/v = 60. Substituting v gives (L+300)/(L/30) = 60, so L+300 = 2L, hence L = 300m. Quantity II: Train speed = v = 200/25 = 8 m/s. Crossing platform in 55s: (200+P)/8 = 55, so 200+P = 440, hence P = 240m. Comparing: 300 > 240, so Quantity I > Quantity II.

Multiple choice

How many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km/hr. in the opposite direction of the moving train if the speed of the train is 72 km/hr.? 500 मीटर लंबी ट्रेन चलती ट्रेन की विपरीत दिशा में 3 किमी / घंटा की रफ्तार से चलने वाले व्यक्ति को पार करने में कितने सेकेण्ड लेगी। यदि ट्रेन की गति 72 किमी / घंटा है?

  1. 12 sec./से.

  2. 24 sec./से.

  3. 35 sec./से.

  4. 45 sec./से.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Relative speed = 72 + 3 = 75 km/hr (opposite direction, speeds add). Convert to m/s: 75 × (5/18) = 375/18 = 125/6 m/s. Time = Distance/Speed = 500/(125/6) = 500 × 6/125 = 24 seconds. Option A (12 sec) ignores units conversion. Options C and D are calculation errors.

Multiple choice

What is the speed of a train? (I) The train crossing a platform double its length in 48 sec. (II) The length of the train is 360 m. (III) The train crosses a man in 16 sec.

  1. Only I

  2. Only II

  3. Either I & II together or I & III together

  4. Only III

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

Neither statement combination is sufficient. I+III alone fails (2 equations, 3 unknowns: speed, train length, platform length). II+III gives speed = 360/16 = 22.5 m/s, but without I we can't verify against the platform condition. The question asks 'What is speed?' - all options are incorrect as some data exists but none are sufficient.

Multiple choice

A train 280 m. long is moving at a speed of 60 km./hr. What is the time taken by the train to cross a platform 220 m. long? एक 280 मी. लम्बी रेलगाड़ी 60 किमी./घं. की रफ्तार से चल रही है। किसी 220 मी. लम्बे प्लेटफार्म को पार करने में उस रेलगाड़ी को कितना समय लगता है?

  1. 45 seconds/सेकेण्ड

  2. 40 seconds/सेकेण्ड

  3. 35 seconds/सेकेण्ड

  4. 30 seconds/सेकेण्ड
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total distance to cross = train length + platform length = 280 + 220 = 500 m. Speed = 60 km/hr = 60 × (5/18) = 50/3 m/s. Time = Distance/Speed = 500 ÷ (50/3) = 500 × 3/50 = 30 seconds. This is a standard train-platform problem requiring unit conversion.

Multiple choice

The length of two trains (T_1) and (T_2) be the ratio of 5:6 and the length of platform is 1500m. The train (T_1) crosses a platform in 50sec and train (T_2) crosses a platform in 30sec. The speed of train (T_1) is 50 m/sec. Find the ratio of speed trains (T_1) and (T_2).

  1. 5:3

  2. 3:5

  3. 5:9

  4. 3:2

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

T1 length: Distance = speed × time = 50 × 50 = 2500m. So platform (1500m) + T1 length = 2500m, giving T1 = 1000m. Since T1:T2 = 5:6, T2 = (6/5) × 1000 = 1200m. T2 crosses same platform: Distance = 1500 + 1200 = 2700m in 30s, so speed = 2700/30 = 90 m/s. Ratio T1:T2 = 50:90 = 5:9.

Multiple choice

A train, 125 m long is running at a speed of 90 km/hr. How many seconds does it take to cross another train, 210 m long, standing on parallel track?

  1. 14.2 second

  2. 13.4 second

  3. 14.9 second

  4. 13.0 second
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Speed = 90 km/hr = 25 m/s. Total distance to cover = length of moving train + length of stationary train = 125 + 210 = 335 m. Time = Distance/Speed = 335/25 = 13.4 seconds. Since the other train is stationary, relative speed is just the moving train's speed.

Multiple choice

At what time will the train reach city X from city Y? Statement I: The train crosses another goods train of equal length of 150 meters running in the same directions in 90 seconds. Statement II: The train leaves city Y at 8:40 a.m. for city X situated at a distance of 600 km. Statement III: The 150 meters long train crosses a signal pole in 20 seconds.

  1. I and II

  2. II and III

  3. Any two

  4. All three together are sufficient

  5. All three together are not sufficient
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement III gives train length (150m) and time to cross pole (20s), so speed = 150/20 = 7.5 m/s. Statement II gives distance (600km) and departure time (8:40 a.m.). Time = 600,000m / 7.5 m/s = 80,000s = 22h 13m 20s. Arrival ≈ 8:40 + 22h 13m = 6:53 p.m. next day. Statements II and III are sufficient. Statement I is unnecessary.

Multiple choice

A 330 meter long train crosses another 150 meter long train in 55 seconds. If the speed of one train is 24 km/hr, what is the speed of the second train?

  1. 12 km/hr

  2. 24 km/hr

  3. 36 km/hr

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

Total distance = 480m. Time = 55s. Relative speed = 480/55 m/s ≈ 31.42 km/hr. If one train is 24 km/hr, the other could be 7.42 km/hr (opposite direction) or 55.42 km/hr (same direction). The problem doesn't specify direction, and neither calculated value matches options A (12), B (24), or C (36). Thus, data is inadequate.

Multiple choice

A train of length 700 m. passes through a tunnel whose length is 500 meters in 1 minute. The speed of the train is- एक 700 मी. लम्बी रेलगाड़ी 500 मी. लम्बी सुरंग को 1 मिनट में पार करती है। रेलगाड़ी की चाल है-

  1. 60 kmph/किमी./घंटा

  2. 64 kmph/किमी./घंटा

  3. 72 kmph/किमी./घंटा

  4. 75 kmph/किमी./घंटा
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total distance to pass through tunnel = train length + tunnel length = 700 + 500 = 1200 meters. Time taken = 1 minute = 60 seconds. Speed = Distance/Time = 1200/60 = 20 m/s. Convert to kmph: 20 × (18/5) = 72 kmph. The train must travel its own length plus the tunnel length to completely clear the tunnel.

Multiple choice

A train moving at the speed of 80 km/hr crosses a platform in 20 seconds. What is the length of the train?

  1. 330 m

  2. 336 m

  3. 360 m

  4. Cannot be determined

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

The length of the train cannot be determined from the given information. To find train length, we need either the length of the platform or the total distance covered (train length + platform length). The formula is: Distance = Speed × Time. Here, Speed = 80 km/hr = 80 × (5/18) m/s ≈ 22.22 m/s. Distance covered in 20 seconds = 22.22 × 20 ≈ 444.44 m. But this is the train length PLUS platform length. Without knowing the platform length, we cannot find the train length alone.

Multiple choice

A and B are two stations 500 km apart. A train starts from A and moves towards B at 20 km/hour. Another train starts from B at the same time and moves towards A at 30 km/hour. The distance of the crossing point of the two trains from A (in km) is.

  1. 100

  2. 200

  3. 250

  4. 300
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Trains approach each other at 20 + 30 = 50 km/hour. Time to meet: 500/50 = 10 hours. Distance from A: 20 × 10 = 200 km. The crossing point is closer to A because the train from A is slower.

Multiple choice

‘A’, a 320 m long train crosses a pole in 50 seconds, whereas train ‘B’ crosses this pole in 100 seconds. Find the ratio of speed of train ‘A’ to train ‘B’.
  1. $2 : 1$
  2. $4 : 1$
  3. $1 : 2$

  4. None of these

  5. Can’t be determined
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Speed = Distance/Time. For train A, speed = 320/50 = 6.4 m/s. For train B, we only know the time to cross the pole (100 seconds), but we don't know the length of train B. Without the distance information (length of train B), we cannot determine its speed, making the ratio of speeds impossible to calculate.