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 220 m. long train is running with a speed of 62 km./hr. What is the time in which it will cross a man running at the speed of 4 km./hr. who starts from the engine in the direction opposite to that of the train?

  1. 16 sec.

  2. 12 sec.

  3. 10 sec.

  4. 15 sec.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The train length is 220 m and its speed is 62 km/hr. The man runs opposite to the train at 4 km/hr. Relative speed = 62 + 4 = 66 km/hr = (66 × 5/18) m/s = 55/3 m/s. Time = Distance/Speed = 220 ÷ (55/3) = 220 × 3/55 = 12 seconds. Since the man starts from the engine and runs opposite to the train, he needs to cover the entire train length.

Multiple choice

Two trains which are 150 m long each are moving in opposite directions. They cross each other in 12 seconds. If one train is moving two and a half times as fast the other train, then find the speed of the faster train.

  1. 125 km/hr.

  2. 132 km/hr.

  3. 168 km/hr.

  4. 172 km/hr.

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

Total distance = 150 + 150 = 300 m. Relative speed = 300/12 = 25 m/s = 90 km/hr. Let slower train speed = v, then faster = 2.5v. So v + 2.5v = 3.5v = 90 km/hr. Therefore v = 90/3.5 ≈ 25.7 km/hr and faster train = 2.5 × 25.7 ≈ 64.3 km/hr. None of the given options (125, 132, 168, 172) match this result.

Multiple choice

A train of length 135 meter crosses a man coming from opposite direction with a speed of 8 Km/h in 9 seconds. Find the time taken by train to cross a another passenger train whose length is 150 meters and also coming from opposite direction with speed of 14 Km/h.(In seconds) 135 मीटर लंबाई की एक ट्रेन 8 किमी/घंटा की गति के साथ विपरीत दिशा से आ रहे एक व्यक्ति को 9 सेकेंड में पार करती है। इसी ट्रेन दारा विपरीत दिशा से 14 किमी/घंटा की गति से आ रही दूसरी पैसेंजर ट्रेन जिसकी लम्बाई 150 मीटर को पार करने में लगे समय को गणना कीजिये? (सेकंड में)

  1. 16.8

  2. 15.5

  3. 14.2

  4. 17.1
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

First find the train's speed: when crossing the man, relative speed = (train speed + 8 km/h) = 135/9 = 15 m/s = 54 km/h. So train speed = 54 - 8 = 46 km/h. When crossing the other train, relative speed = 46 + 14 = 60 km/h = 60 × 5/18 = 50/3 m/s. Time = (135 + 150)/(50/3) = 285 × 3/50 = 17.1 seconds.

Multiple choice

In each of the following questions, a question is followed by three statements numbered I, II and III. Read all the statements and find which information is/are necessary to answer. What is the speed of the train? I. Length of the train is 300 meters. II. The train crosses a platform double of its length in 54 sec. III. The train crosses a signal pole in 18 sec

  1. All three together are sufficient

  2. II and III together

  3. I and III together

  4. All three together are not sufficient

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

From Statement I and III: Length = 300m, crosses pole in 18s. Speed = 300/18 = 50/3 m/s. From II and III: Platform length = 2*train length. Crosses in 54s, so 3*length = speed*54. Also crosses pole in 18s, so length = speed*18. Solving: 3*18*speed = 54*speed, consistent. Speed = 50/3 m/s. Both (I,III) and (II,III) work, so E is correct.

Multiple choice

If the speed of the train be 80 kmph and it takes 6 seconds to pass a platform. Next it takes 5 seconds to pass a cyclist walking at the rate of 12 km/hr. In the same direction. What is the length of the platform? यदि एक ट्रेन की चाल 80 किमी प्रति घंटा है और वह एक प्लेटफार्म को 6 सेकेन्ड में पार करता है। उसी दिशा में 12 किमी/घंटा के चाल से जा रहे एक साइकिल सवार को 5 सेकेन्ड में पार करता है। प्लेटफार्म की लम्बाई कितनी मीटर है?

  1. 38.88

  2. 35.56

  3. 48.56

  4. 32.35
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

ट्रेन की चाल = 80 किमी/घंटा = 80×5/18 = 22.22 मीटर/सेकंड। साइकिल सवार की चाल = 12 किमी/घंटा = 12×5/18 = 3.33 मीटर/सेकंड। सापेक्ष चाल (समान दिशा) = 22.22 - 3.33 = 18.89 मीटर/सेकंड। ट्रेन की लंबाई = 18.89 × 5 = 94.45 मीटर (गलत दृष्टिकोण)। सही विधि: प्लेटफार्म पार करने में: ट्रेन की लंबाई + प्लेटफार्म की लंबाई = 22.22 × 6 = 133.32 मीटर। साइकिल सवार को पार करने में: ट्रेन की लंबाई = (22.22 - 3.33) × 5 = 94.45 मीटर। प्लेटफार्म की लंबाई = 133.32 - 94.45 = 38.87 ≈ 38.88 मीटर। विकल्प A सही है।

Multiple choice

(\text{Find the values and state the correct relationship.}\\text{Quantity I: The length of train if train can cross a pole in 18 seconds and a 210 m platform in 39 seconds.}\\text{Quantity II: The length of platform if 200 m long train passes a pole in 20 seconds and platform in 46 seconds})

  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
C Correct answer
Explanation

Quantity I: Train crosses pole in 18 sec, so length L = 18 × speed. Crosses 210 m platform in 39 sec, so L+210 = 39 × speed. Subtracting: 210 = 21 × speed, so speed = 10 m/s. Therefore L = 18 × 10 = 180 m. Quantity II: 200 m train crosses pole in 20 sec, so speed = 10 m/s. Platform length P satisfies 200+P = 46 × 10 = 460, so P = 260 m. Comparing: 180 < 260, so Quantity II > Quantity I.

Multiple choice

The sum of the lengths of two trains A and B is 696 m. The ratio of the speed of A to that of B is 6 : 7. The ratio of the time to cross an electric pole by train A to that by B is 5 : 4. Find the difference between the lengths of the two trains (in meter).

  1. 18

  2. 27

  3. 24

  4. 20

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

Let lengths be LA and LB. LA + LB = 696. Time = length/speed, so LA/SA : LB/SB = 5:4. Given SA:SB = 6:7, then LA:LB = 15:14. So LA = 360m, LB = 336m. Difference = 24m. Option C matches.

Multiple choice

Two trains while moving in opposite direction on parallel tracks, take 10 seconds to cross each other. However, if they travel in the same direction, the longer train, which is faster than the shorter train, crosses the shorter train in 30 seconds. If the length of the longer train is decreased by 75%, it takes 12 seconds less to cross the shorter train traveling in the same direction. Find the time taken by the longer train to cross a tunnel twice its length, if the difference between the lengths of the trains is 50 m?

  1. 28 seconds

  2. 20 seconds

  3. 24 seconds

  4. 32 seconds

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

Let longer train length = L, shorter = S, speeds = Vl, Vs. Opposite direction: (L+S)/(Vl+Vs) = 10. Same direction: (L+S)/(Vl-Vs) = 30. Reduced length: (0.25L+S)/(Vl-Vs) = 18. Also L - S = 50. From first two equations: 10(Vl+Vs) = 30(Vl-Vs), so Vl = 2Vs. Using this and the equations, we find Vs = 25, Vl = 50, L = 400. Tunnel length = 2L = 800, crossing time = (L+2L)/Vl = 3L/Vl = 1200/50 = 24 seconds.

Multiple choice

A train crosses another train in 10 sec. Find out the lengths of the trains. A. Ratio between the lengths of the second and first train is 4: 5. B. Ratio between the speed of first and second trains is 1: 2. C. The speed of the first train is 36 km/hr

  1. Only A and B together

  2. Only B and C together

  3. Only A and C together

  4. Questions can’t be answered even after using all the information

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

We have ratios (length and speed) and individual train speeds, but never the total distance covered while crossing. We need either: (relative speed × time) = sum of lengths, or a specific length value. Neither is provided. Even with all statements, we cannot find the lengths.

Multiple choice

Each question below contains a statement followed by Quantity I and Quantity II. Find both to find the relationship among them. Mark your answer accordingly. Quantity I: The length of train if train can cross a pole in 18 seconds and a 210 m platform in 39 seconds. Quantity II: The length of platform if 200 m long train passes a pole in 20 seconds and platform in 46 seconds.

  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
C Correct answer
Explanation

Quantity I: Train speed = 210÷(39-18) = 10 m/s. Length = 10×18 = 170 m. Quantity II: Train speed = 200÷20 = 10 m/s. Platform length = 10×46 - 200 = 260 m. 260 > 170, so Quantity II is greater.

Multiple choice

Find the value of Q1 and Q2 and state the correct relationship. Quantity I: Time taken by A to complete 1/5th of work if B takes 6 days to complete 3/5th of work and together they take 5 days to complete 3/4th of work Quantity II: Time taken by a train to cross a platform of length 60 km given that it crosses a pole in two and a half hours running at 60 km/hr

  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: B takes 6 days for 3/5 work, so B's rate = (3/5)/6 = 1/10 per day. B takes 10 days alone. A + B together take 5 days for 3/4 work, so combined rate = (3/4)/5 = 3/20 per day. A's rate = 3/20 - 1/10 = 1/20 per day. A takes 20 days alone. For 1/5 work: time = (1/5)/(1/20) = 20/5 = 4 days. Quantity II: Train crosses a pole (its own length) in 2.5 hours at 60 km/hr. So train length = 60 × 2.5 = 150 km. Wait - that's very long for a train. Let me reconsider: crossing time = length/speed, so length = speed × time = 60 × 2.5 = 150 km. To cross a 60 km platform: distance = 150 + 60 = 210 km. Time = 210/60 = 3.5 hours. Comparing: Quantity I = 4 days, Quantity II = 3.5 hours. 4 days > 3.5 hours, so Quantity I is greater.

Multiple choice

Two trains with their speeds in the ratio of 3 : 4 are going in opposite directions along parallel tracks. If each takes 9 seconds to cross a telegraph post, then the time taken by the trains, to cross each other completely, will be दो रेलगाड़ियाँ, जिनकी गति का अनुपात 3 : 4 है, समानान्तर पटरियों पर विपरीत दिशा से चलते हुए एक दूसरे की ओर आ रही है।अगर प्रत्येक रेलगाड़ी 9 सेकेण्ड में एक टेलीग्राफ पोस्ट को पार करती है तो एक-दूसरे को पार करने में उन्हें कितना समय लगेगा?

  1. 9 seconds/सेकेण्ड

  2. 3 seconds/सेकेण्ड

  3. 18 seconds/सेकेण्ड

  4. 12 seconds/सेकेण्ड
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let speeds be 3x and 4x. From crossing telegraph posts in 9 seconds, lengths are 27x and 36x respectively. When crossing each other in opposite directions, relative speed = 3x + 4x = 7x. Total distance = 27x + 36x = 63x. Time = distance/speed = 63x/7x = 9 seconds.

Multiple choice

How many seconds will a 800 m long train take to cross a man walking with a speed of 5 km/hr. in the direction of the moving train if the speed of train is 65 km/hr.? 800 मीटर लम्बी एक रेलगाड़ी को 5 किमी/घं. की चाल से उसकी दिशा में पैदल चलते व्यक्ति को पार करने में कितना समय (सेकण्ड में) लगेगा, यदि रेलगाड़ी 65 किमी/घंटे की चाल से चल रही है?

  1. 30 seconds/सेकेण्ड

  2. 36 seconds/सेकेण्ड

  3. 48 seconds/सेकेण्ड

  4. 42 seconds/सेकेण्ड
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Relative speed = 65 - 5 = 60 km/hr = 60 × (5/18) = 50/3 m/s. Time = distance/speed = 800 ÷ (50/3) = 800 × 3/50 = 48 seconds.

Multiple choice

A train reaches its destination on time with an average speed of 40 kmph. If it goes with an average speed of 35 kmph, it is late by 15 minutes. Find the length of the total journey.

  1. 70 km

  2. 56 km

  3. 23 km

  4. 78 km

  5. 85 km
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let distance = d km. At 40 kmph, time = d/40 hours. At 35 kmph, time = d/35 hours. The difference is 15 minutes = 15/60 = 1/4 hours. So d/35 - d/40 = 1/4. d(1/35 - 1/40) = 1/4. d(40 - 35)/(35 × 40) = 1/4. d(5)/(1400) = 1/4. d/280 = 1/4. Therefore d = 280/4 = 70 km.

Multiple choice

A train 180 m. long moving at the speed of 20 m./sec. over takes a man moving at a speed of 10 m./sec. in the same direction. The train passes the man in - एक 180 मी. लम्बी रेलगाड़ी 20 मी./से. की चाल से एक व्यक्ति को जोकि समान दिशा में 10 मी./सेकेण्ड की चाल से चल रहा है, पार करती है। रेलगाड़ी व्यक्ति को कितने समय में पार करती है-

  1. 9 seconds

  2. 18 seconds

  3. 13 seconds

  4. 27 seconds
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When a train overtakes a person moving in the same direction, use relative speed. The train's speed minus the person's speed gives relative speed: 20 - 10 = 10 m/s. The train must cover its own length (180m) at this relative speed. Time = Distance / Speed = 180 / 10 = 18 seconds. Option A (9s) would be the result if you used 20 m/s without subtracting the man's speed. Option D (27s) might come from adding the speeds incorrectly.