Problems ON Trains Aptitude Placement

Last Updated: March 2026

Introduction to Problems on Trains

Problems on Trains is one of the most frequently asked topics in aptitude tests for campus placements. This topic tests your ability to calculate relative speed, time, and distance when trains are involved. Understanding the core concepts is crucial as these questions appear in almost every major company placement exam including TCS, Infosys, Wipro, Cognizant, Accenture, and others.

Why This Topic is Important

Train problems form the backbone of Time, Speed, and Distance questions. Companies use these questions to assess:

Your understanding of relative motion
Ability to visualize scenarios
Quick calculation skills
Application of formulas in practical situations

Companies That Ask Train Problems (with Frequency)

Company	Frequency	Difficulty Level
TCS	Very High	Easy to Moderate
Infosys	Very High	Easy to Moderate
Wipro	High	Easy
Cognizant	High	Easy to Moderate
Accenture	High	Easy
Capgemini	Moderate	Easy
IBM	Moderate	Moderate
Tech Mahindra	High	Easy
HCL	Moderate	Easy to Moderate
LTI Mindtree	Moderate	Easy

KEY FORMULAS / CONCEPTS

╔══════════════════════════════════════════════════════════════════╗
║                     TRAINS FORMULA SHEET                         ║
╠══════════════════════════════════════════════════════════════════╣
║                                                                  ║
║  Basic Formula:                                                  ║
║  Speed = Distance / Time                                        ║
║                                                                  ║
║  Conversion:                                                     ║
║  1 km/hr = 5/18 m/s                                             ║
║  1 m/s = 18/5 km/hr = 3.6 km/hr                                 ║
║                                                                  ║
║  ═══════════════════════════════════════════════════════════    ║
║                                                                  ║
║  CASE 1: Train crossing a stationary object (pole/person)       ║
║  Time = Length of Train / Speed of Train                        ║
║                                                                  ║
║  CASE 2: Train crossing a platform/bridge/station               ║
║  Time = (Length of Train + Length of Platform) / Speed          ║
║                                                                  ║
║  CASE 3: Two trains moving in OPPOSITE directions               ║
║  Relative Speed = S₁ + S₂                                       ║
║  Time to cross = (L₁ + L₂) / (S₁ + S₂)                          ║
║                                                                  ║
║  CASE 4: Two trains moving in SAME direction                     ║
║  Relative Speed = |S₁ - S₂|                                     ║
║  Time to cross = (L₁ + L₂) / |S₁ - S₂|                          ║
║                                                                  ║
║  CASE 5: Train crossing a moving object (person/train)          ║
║  Same direction: Relative Speed = |S_train - S_object|          ║
║  Opposite direction: Relative Speed = S_train + S_object        ║
║                                                                  ║
╚══════════════════════════════════════════════════════════════════╝

30 Practice Questions with Step-by-Step Solutions

Question 1

A train 150 m long is running at a speed of 90 km/hr. How long will it take to cross a pole?

Solution: Speed = 90 km/hr = 90 × (5/18) = 25 m/s Time = Length/Speed = 150/25 = 6 seconds

Question 2

A train 200 m long passes a pole in 10 seconds. Find the speed of the train in km/hr.

Solution: Speed = Distance/Time = 200/10 = 20 m/s In km/hr = 20 × (18/5) = 72 km/hr

Question 3

A train running at 54 km/hr crosses a platform 150 m long in 20 seconds. Find the length of the train.

Solution: Speed = 54 × (5/18) = 15 m/s Total distance = Speed × Time = 15 × 20 = 300 m Length of train = 300 - 150 = 150 m

Question 4

A 300 m long train crosses a platform in 30 seconds and a pole in 15 seconds. Find the length of the platform.

Solution: Speed = 300/15 = 20 m/s Total distance (train + platform) = 20 × 30 = 600 m Platform length = 600 - 300 = 300 m

Question 5

Two trains 200 m and 150 m long are running on parallel tracks in opposite directions at 40 km/hr and 50 km/hr respectively. How long will they take to cross each other?

Solution: Relative speed = 40 + 50 = 90 km/hr = 90 × (5/18) = 25 m/s Total length = 200 + 150 = 350 m Time = 350/25 = 14 seconds

Question 6

Two trains of equal length (300 m each) are running on parallel tracks in the same direction at 60 km/hr and 40 km/hr. How long will the faster train take to cross the slower train?

Solution: Relative speed = 60 - 40 = 20 km/hr = 20 × (5/18) = 50/9 m/s Total length = 300 + 300 = 600 m Time = 600 × 9/50 = 108 seconds

Question 7

A train 240 m long passes a pole in 12 seconds. How long will it take to pass a platform 360 m long?

Solution: Speed = 240/12 = 20 m/s Total distance = 240 + 360 = 600 m Time = 600/20 = 30 seconds

Question 8

A train crosses a bridge of length 400 m in 30 seconds and a pole in 10 seconds. Find the length of the train.

Solution: Let length = L, Speed = L/10 (L + 400)/(L/10) = 30 10(L + 400)/L = 30 10L + 4000 = 30L 20L = 4000 L = 200 m

Question 9

A train 180 m long running at 72 km/hr crosses a tunnel in 25 seconds. Find the length of the tunnel.

Solution: Speed = 72 × (5/18) = 20 m/s Total distance = 20 × 25 = 500 m Tunnel length = 500 - 180 = 320 m

Question 10

Two trains start at the same time from stations 450 km apart and proceed towards each other at 50 km/hr and 40 km/hr. When will they meet?

Solution: Relative speed = 50 + 40 = 90 km/hr Time = 450/90 = 5 hours

Question 11

A train overtakes two persons walking in the same direction at 3 km/hr and 5 km/hr, passing them completely in 10 seconds and 11 seconds respectively. Find the speed of the train.

Solution: Let speed = S km/hr, length = L m L/((S-3)×(5/18)) = 10 and L/((S-5)×(5/18)) = 11 (S-3)×(50/18) = (S-5)×(55/18) 50(S-3) = 55(S-5) 50S - 150 = 55S - 275 5S = 125 S = 25 km/hr

Question 12

A train 320 m long takes 40 seconds to cross a platform 480 m long. What is the speed of the train?

Solution: Total distance = 320 + 480 = 800 m Speed = 800/40 = 20 m/s = 20 × (18/5) = 72 km/hr

Question 13

Two trains of lengths 400 m and 300 m are running in opposite directions. The faster train crosses the slower train in 14 seconds. If the speed of the slower train is 60 km/hr, find the speed of the faster train.

Solution: Let faster train speed = S km/hr Relative speed = (S + 60) × (5/18) m/s Total length = 700 m 700 = (S + 60) × (5/18) × 14 S + 60 = 700 × 18/(5 × 14) = 180 S = 120 km/hr

Question 14

A train travels first 150 km at 75 km/hr, next 120 km at 60 km/hr, and last 90 km at 45 km/hr. Find the average speed.

Solution: Total distance = 360 km Total time = 150/75 + 120/60 + 90/45 = 2 + 2 + 2 = 6 hours Average speed = 360/6 = 60 km/hr

Question 15

A train 250 m long is running at 90 km/hr. How long will it take to pass a man running at 18 km/hr in the same direction?

Solution: Relative speed = 90 - 18 = 72 km/hr = 72 × (5/18) = 20 m/s Time = 250/20 = 12.5 seconds

Question 16

Two stations A and B are 330 km apart. A train starts from A at 8 a.m. at 60 km/hr towards B. Another train starts from B at 9 a.m. at 75 km/hr towards A. When will they meet?

Solution: By 9 a.m., first train covers 60 km. Remaining = 270 km Relative speed = 60 + 75 = 135 km/hr Time = 270/135 = 2 hours after 9 a.m. They meet at 11 a.m.

Question 17

A train passes a man standing on a platform in 8 seconds and crosses the platform 250 m long in 18 seconds. Find the length and speed of the train.

Solution: Let length = L, Speed = L/8 (L + 250)/(L/8) = 18 8(L + 250)/L = 18 8L + 2000 = 18L 10L = 2000, L = 200 m Speed = 200/8 = 25 m/s = 90 km/hr

Question 18

A goods train leaves a station at a certain time and at a fixed speed. After 6 hours, an express train leaves the same station and moves in the same direction at 90 km/hr, catching the goods train in 4 hours. Find the speed of the goods train.

Solution: Let goods train speed = S km/hr Distance covered by goods train in 10 hours = 10S Distance covered by express train in 4 hours = 4 × 90 = 360 km 10S = 360, S = 36 km/hr

Question 19

Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 72 seconds. Find the length of each train.

Solution: Relative speed = 46 - 36 = 10 km/hr = 10 × (5/18) = 25/9 m/s Let length = L, Total length = 2L 2L = (25/9) × 72 = 200 L = 100 m

Question 20

A train 180 m long running at 60 km/hr crosses a man walking at 6 km/hr in the opposite direction. Find the time taken.

Solution: Relative speed = 60 + 6 = 66 km/hr = 66 × (5/18) = 55/3 m/s Time = 180 × 3/55 = 9.82 seconds (approx 10 seconds)

Question 21

A train running at 54 km/hr takes 20 seconds to pass a platform. Next, it takes 12 seconds to pass a man walking at 6 km/hr in the same direction. Find the length of the train and the platform.

Solution: Let train length = L, Platform = P Speed = 54 × (5/18) = 15 m/s (L + P)/15 = 20 → L + P = 300 Relative speed with man = (54-6) × (5/18) = 48 × (5/18) = 40/3 m/s L/(40/3) = 12 → L = 160 m P = 300 - 160 = 140 m Train = 160 m, Platform = 140 m

Question 22

Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. Find the time taken to cross each other.

Solution: Relative speed = 60 + 90 = 150 km/hr Total length = 1.10 + 0.9 = 2 km Time = 2/150 hours = (2/150) × 3600 = 48 seconds

Question 23

A train covers a distance of 12 km in 10 minutes. If it takes 6 seconds to pass a telegraph post, find the length of the train.

Solution: Speed = 12 km / (10/60) hr = 72 km/hr = 72 × (5/18) = 20 m/s Length = Speed × Time = 20 × 6 = 120 m

Question 24

A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a man running at 6 km/hr in the opposite direction?

Solution: Relative speed = 60 + 6 = 66 km/hr = 66 × (5/18) = 55/3 m/s Time = 110 × 3/55 = 6 seconds

Question 25

Two trains 140 m and 160 m long run at speeds of 60 km/hr and 40 km/hr respectively in opposite directions. Find the time they take to cross each other.

Solution: Relative speed = 60 + 40 = 100 km/hr = 100 × (5/18) = 250/9 m/s Total length = 300 m Time = 300 × 9/250 = 10.8 seconds

Question 26

A train 300 m long crossed a platform 900 m long in 1 minute. Find the speed of the train in km/hr.

Solution: Total distance = 1200 m, Time = 60 seconds Speed = 1200/60 = 20 m/s = 20 × (18/5) = 72 km/hr

Question 27

A man sitting in a train which is traveling at 50 km/hr observes that a goods train traveling in the opposite direction takes 9 seconds to pass him. If the goods train is 280 m long, find its speed.

Solution: Let speed of goods train = S km/hr Relative speed = (50 + S) × (5/18) m/s 280 = (50 + S) × (5/18) × 9 280 = (50 + S) × 2.5 50 + S = 112, S = 62 km/hr

Question 28

A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Find the length of the train.

Solution: Let length = L, Speed = L/15 (L + 100)/(L/15) = 25 15(L + 100) = 25L 15L + 1500 = 25L 10L = 1500, L = 150 m

Question 29

Two trains start simultaneously from Howrah to Patna and Patna to Howrah. After meeting, they reach their destinations in 9 hours and 16 hours respectively. Find the ratio of their speeds.

Solution: If two trains start from A and B and meet, then: (Speed of A)/(Speed of B) = √(Time taken by B after meeting)/√(Time taken by A after meeting) = √16/√9 = 4/3 Ratio = 4:3

Question 30

A train 150 m long takes 10 seconds to pass a man walking at 5 km/hr in the opposite direction. Find the speed of the train.

Solution: Let train speed = S km/hr Relative speed = (S + 5) × (5/18) m/s 150 = (S + 5) × (5/18) × 10 150 = (S + 5) × 25/9 S + 5 = 54, S = 49 km/hr (Or 50 km/hr approx)

SHORTCUTS & TRICKS

Trick 1: Quick Conversion

km/hr to m/s: Multiply by 5/18
m/s to km/hr: Multiply by 18/5

Memory Tip: "5-18 is the magic number!"

Trick 2: Same Length Trains

When two trains of equal length L cross each other:

Opposite direction: Time = 2L/(S₁+S₂)
Same direction: Time = 2L/|S₁-S₂|

Trick 3: Finding Speed from Two Observations

If a train takes t₁ seconds for length L₁ and t₂ seconds for length L₂: Speed = (L₂ - L₁)/(t₂ - t₁)

Trick 4: Man Walking Problems

When a train passes a walking man:

Same direction: Subtract speeds
Opposite direction: Add speeds

Trick 5: Quick Platform Length

If train length = L, speed = S m/s, time to cross platform = T: Platform length = (S × T) - L

Trick 6: Two Trains Meeting

When trains start simultaneously from A and B: Meeting time = Distance/(S₁ + S₂)

Trick 7: Late/Early Problems

Use the formula: (S₁ × S₂ × Δt)/|S₁ - S₂| = Distance difference

Trick 8: Ratio of Speeds After Meeting

If trains meet and reach destinations in t₁ and t₂ hours: S₁/S₂ = √t₂/√t₁

Common Mistakes to Avoid

Unit Confusion: Always convert km/hr to m/s when length is in meters. Multiply by 5/18, not 18/5!
Total Distance Error: When crossing a platform/bridge, remember to ADD both lengths, not just use one.
Relative Speed Direction:
- Opposite direction = ADD speeds
- Same direction = SUBTRACT speeds
Time Calculation: Ensure time is in seconds when speed is in m/s.
Man/Platform Confusion: A man/pole has negligible length compared to a train.
Starting Time Differences: Account for head start when one train leaves earlier.
Average Speed Trap: Don't take arithmetic mean! Use: Total Distance/Total Time.

5 Frequently Asked Questions

Q1: How do I quickly convert between km/hr and m/s? A: Remember 5/18! km/hr → m/s: × 5/18. m/s → km/hr: × 18/5. Think: "Kilometer is bigger, so number gets smaller when converting to m/s."

Q2: What is the most common mistake in train problems? A: Forgetting to add the length of the train when crossing platforms. Total distance = Train length + Platform length.

Q3: How do I approach problems with trains and walking persons? A: Treat the person as an object with negligible length. Calculate relative speed based on direction (add if opposite, subtract if same).

Q4: Do I need to memorize all formulas? A: No, just understand relative speed concept. The rest follows: Time = Total Distance/Relative Speed.

Q5: How much time should I spend on each train problem in the exam? A: Aim for 45-60 seconds per question. If stuck beyond 90 seconds, mark for review and move on.

Best of luck with your placement preparation! Practice these 30 questions multiple times to master the concepts.

Frequently Asked Questions

In most Indian campus placements, aptitude topics like “Problems on Trains” are used to shortlist candidates rather than determine a separate salary band. Your final CTC depends mainly on your overall performance across aptitude, coding/DSA (if applicable), and interviews. For Placement 2026, companies generally offer a wide range (often from entry-level packages to higher offers for top performers), so strong aptitude accuracy can improve your chances of reaching higher stages.

Who is eligible to attempt Problems on Trains questions for Placement 2026 preparation?

Eligibility is usually based on your academic status (e.g., being in the final year or eligible for campus drives) rather than topic-specific prerequisites. For aptitude preparation, you only need basic arithmetic and algebra concepts like speed, time, distance, ratios, and simple equations. Any student from engineering, BCA, or similar backgrounds can practice these questions effectively with the right formula approach.

How difficult are Problems on Trains questions in placement exams?

They are considered medium difficulty overall: the core formulas are simple, but questions often become tricky due to multiple trains, relative speed, and overlapping time intervals. Difficulty increases when problems include trains crossing platforms, trains meeting after passing, or scenarios involving different speeds and directions. With consistent practice, you can reduce calculation errors and improve speed.

What are the best preparation tips for Problems on Trains for Placement 2026?

Start by mastering the standard cases: trains moving in the same direction, opposite directions, and crossing each other with/without platform length. Then practice mixed sets daily and focus on time-saving methods like writing “relative speed” clearly and using a consistent variable setup. Finally, revise solutions and maintain an error log (common mistakes like sign errors, unit mismatch, or wrong distance interpretation).

How many interview rounds typically include aptitude topics like Problems on Trains?

Aptitude topics are most commonly tested in the written test/online assessment stage, which is usually the first major screening round. Some companies may also include similar quantitative questions in subsequent rounds or in the coding/MCQ sections, but “Problems on Trains” is rarely asked in technical interviews. Therefore, your goal should be to perform strongly in the initial assessment to qualify for later rounds.

What common topics appear alongside Problems on Trains in placement aptitude tests?

You’ll often see related quantitative topics such as time and work, speed-time-distance, boats and streams, pipes and cisterns, averages, ratios, and simple algebra. Many exams combine these in mixed sections, so practicing “train + related speed problems” helps you handle variations quickly. Companies also frequently test logical reasoning and basic arithmetic accuracy in the same test.

How can I apply for campus placements and ensure I’m ready for Problems on Trains questions?

To apply, follow your college’s placement cell process and register on the company’s campus portal or through the official placement drive link. For readiness, build a focused aptitude plan: solve daily train problems, take timed mock tests, and review solutions immediately. If your college provides mock assessments, use them to gauge your accuracy and speed before the final placement drive.

What selection rate can I expect if I’m strong in Problems on Trains questions?

There is no fixed “selection rate” tied only to one topic because final selection depends on overall performance across aptitude, coding/technical rounds, and interviews. However, being consistently accurate in speed-time-distance questions can improve your score in the screening stage, which directly affects your chances of qualifying. In practice, candidates who maintain high accuracy in core aptitude topics often progress further, increasing their effective selection probability.