SSC Problems on Trains Questions with Solutions and Tricks

Problems on Trains is an important application of Time, Speed and Distance. In SSC CGL, CHSL and MTS, one or two train questions appear in almost every shift. All train questions come down to one idea: find the total distance the train must cover and divide it by the speed (or the relative speed). This practice paper gives you 30 train questions with answers and short solutions.

Practice Paper at a Glance

What Are Problems on Trains? Basic Concept in Simple Words

A train has a length, so when it crosses an object, it must cover its own length plus the length of the object. The three common cases are listed below.

• Crossing a pole or a standing man: distance = length of the train.
• Crossing a platform or a bridge: distance = length of the train + length of the platform.
• Crossing another train: distance = sum of the lengths of both trains, and the speed used is the relative speed.

Formulas and Shortcut Tricks for SSC Train Problems

• Convert units: km/h to m/s = multiply by 5/18. m/s to km/h = multiply by 18/5.
• Pole or man: speed = length / time.
• Platform or bridge: speed = (length of train + length of platform) / time.
• Opposite directions: relative speed = speed 1 + speed 2.
• Same direction: relative speed = speed 1 - speed 2 (the faster train overtakes the slower).
• Man or object moving: use the relative speed of the train and the man in the same way.
• Two trains starting from two stations and moving towards each other meet after distance / (sum of speeds).
• Equal length trains crossing a pole in t1 and t2 seconds: time to cross each other in opposite directions = 2 t1 t2 / (t1 + t2) and in the same direction = 2 t1 t2 / (t2 - t1).

Set 1: Pole, Platform and Bridge Questions (Q1–Q10)

Q1. A 150 m long train crosses a pole in 15 seconds. Find its speed in km/h.
Answer: 36 km/h
Solution: Speed = 150 / 15 = 10 m/s = 10 x 18/5 = 36 km/h.

Q2. A 120 m long train running at 54 km/h crosses a pole. How much time does it take?
Answer: 8 seconds
Solution: 54 km/h = 15 m/s. Time = 120 / 15 = 8 seconds.

Q3. A 240 m long train running at 72 km/h crosses a 160 m long platform. How long does it take?
Answer: 20 seconds
Solution: Speed = 20 m/s. Distance = 240 + 160 = 400 m. Time = 400 / 20 = 20 seconds.

Q4. A train takes 20 seconds to cross a 200 m long platform and 10 seconds to cross a pole. Find the length of the train.
Answer: 200 m
Trick: Let length = L. Speed = L/10. (L + 200) / 20 = L/10, so L + 200 = 2L and L = 200 m.

Q5. A 100 m long train running at 36 km/h crosses a bridge in 30 seconds. Find the length of the bridge.
Answer: 200 m
Solution: Speed = 10 m/s. Distance in 30 s = 300 m. Bridge = 300 - 100 = 200 m.

Q6. Convert the speed 90 km/h into m/s.
Answer: 25 m/s
Solution: 90 x 5/18 = 25 m/s.

Q7. A 180 m long train running at 54 km/h crosses a man standing on the platform. How much time does it take?
Answer: 12 seconds
Solution: Speed = 15 m/s. Time = 180 / 15 = 12 seconds.

Q8. A train running at 54 km/h passes a 360 m long platform in 40 seconds. Find the length of the train.
Answer: 240 m
Solution: Distance = 15 x 40 = 600 m. Length of train = 600 - 360 = 240 m.

Q9. A 150 m long train crosses a telegraph post in 6 seconds. Find its speed in km/h.
Answer: 90 km/h
Solution: Speed = 150 / 6 = 25 m/s = 25 x 18/5 = 90 km/h.

Q10. A train running at 45 km/h crosses a pole in 12 seconds. Find the length of the train.
Answer: 150 m
Solution: Speed = 12.5 m/s. Length = 12.5 x 12 = 150 m.

Set 2: Two Trains and Moving Objects (Q11–Q20)

Q11. Two trains of length 125 m each run in opposite directions at 42 km/h and 48 km/h. In how many seconds will they cross each other?
Answer: 10 seconds
Solution: Relative speed = 90 km/h = 25 m/s. Distance = 250 m. Time = 250 / 25 = 10 seconds.

Q12. Two trains of length 150 m and 100 m run in the same direction at 60 km/h and 42 km/h. In how many seconds does the faster train overtake the slower one?
Answer: 50 seconds
Solution: Relative speed = 18 km/h = 5 m/s. Distance = 250 m. Time = 250 / 5 = 50 seconds.

Q13. Two trains of length 200 m and 300 m run in opposite directions at 40 km/h and 32 km/h. In how many seconds will they cross each other?
Answer: 25 seconds
Solution: Relative speed = 72 km/h = 20 m/s. Distance = 500 m. Time = 500 / 20 = 25 seconds.

Q14. Two trains of length 180 m and 120 m run in the same direction at 72 km/h and 36 km/h. How long does the faster train take to overtake the slower train?
Answer: 30 seconds
Solution: Relative speed = 36 km/h = 10 m/s. Distance = 300 m. Time = 300 / 10 = 30 seconds.

Q15. A 110 m long train running at 60 km/h passes a man running at 6 km/h in the opposite direction. How long does it take to pass him?
Answer: 6 seconds
Solution: Relative speed = 66 km/h = 55/3 m/s. Time = 110 / (55/3) = 6 seconds.

Q16. A 150 m long train running at 60 km/h passes a man running at 6 km/h in the same direction. How long does it take to pass him?
Answer: 10 seconds
Solution: Relative speed = 54 km/h = 15 m/s. Time = 150 / 15 = 10 seconds.

Q17. Two trains start from two stations 300 km apart and move towards each other at 45 km/h and 55 km/h. After how many hours do they meet?
Answer: 3 hours
Solution: Relative speed = 100 km/h. Time = 300 / 100 = 3 hours.

Q18. Two trains of equal length take 10 seconds and 15 seconds to cross a telegraph post. If each train is 120 m long, in what time will they cross each other when moving in opposite directions?
Answer: 12 seconds
Trick: Speeds = 12 m/s and 8 m/s. Relative speed = 20 m/s. Distance = 240 m. Time = 12 seconds.

Q19. A 200 m long train running at 90 km/h crosses a 800 m long platform. How long does it take?
Answer: 40 seconds
Solution: Speed = 25 m/s. Distance = 1,000 m. Time = 1,000 / 25 = 40 seconds.

Q20. A train running at 72 km/h takes 20 seconds to cross a stationary train 200 m long. Find the length of the moving train.
Answer: 200 m
Solution: Distance = 20 x 20 = 400 m. Length of moving train = 400 - 200 = 200 m.

Set 3: Exam-Level Train Questions (Q21–Q30)

Q21. A 120 m long train crosses a 180 m long platform in 15 seconds. Find its speed in km/h.
Answer: 72 km/h
Solution: Speed = 300 / 15 = 20 m/s = 72 km/h.

Q22. Two trains start from two stations 360 km apart at 40 km/h and 50 km/h towards each other. How far from the first station do they meet?
Answer: 160 km
Solution: Time = 360 / 90 = 4 hours. Distance from the first station = 40 x 4 = 160 km.

Q23. A train crosses two platforms of length 120 m and 180 m in 10 seconds and 12 seconds respectively. Find the length of the train.
Answer: 180 m
Trick: (L + 120) / 10 = (L + 180) / 12, so 12L + 1,440 = 10L + 1,800 and L = 180 m.

Q24. A 150 m long train passes a 250 m long bridge in 20 seconds. Find its speed in km/h.
Answer: 72 km/h
Solution: Speed = 400 / 20 = 20 m/s = 72 km/h.

Q25. A train takes 6 hours to cover a distance at 60 km/h. At what speed must it run to cover the same distance in 4 hours?
Answer: 90 km/h
Solution: Distance = 360 km. Speed = 360 / 4 = 90 km/h.

Q26. A 300 m long train crosses a pole in 20 seconds. How long will it take to cross a 450 m long platform?
Answer: 50 seconds
Solution: Speed = 15 m/s. Distance = 750 m. Time = 750 / 15 = 50 seconds.

Q27. A 100 m long train overtakes another train 80 m long in 18 seconds. If the slower train runs at 36 km/h, find the speed of the faster train.
Answer: 72 km/h
Solution: Relative speed = 180 / 18 = 10 m/s = 36 km/h. Faster train = 36 + 36 = 72 km/h.

Q28. A man standing on a platform sees a train pass him in 8 seconds. The train takes 20 seconds to cross the platform, which is 300 m long. Find the length of the train.
Answer: 200 m
Trick: Let length = L. L/8 = (L + 300)/20, so 20L = 8L + 2,400 and L = 200 m.

Q29. A train running at 54 km/h takes 20 seconds to cross a bridge 200 m long. Find the length of the train.
Answer: 100 m
Solution: Distance = 15 x 20 = 300 m. Length of train = 300 - 200 = 100 m.

Q30. A 120 m long train crosses a pole in 6 seconds and another train 80 m long crosses a pole in 8 seconds. If they run in opposite directions, in how many seconds will they cross each other?
Answer: 6 2/3 seconds
Solution: Speeds = 20 m/s and 10 m/s. Relative speed = 30 m/s. Distance = 200 m. Time = 200 / 30 = 6 2/3 seconds.

Common Mistakes in Train Problems

• Forgetting to add the length of the platform or the other train.
• Not converting km/h into m/s before using the lengths in metres.
• Adding speeds when the trains move in the same direction.
• Using only the length of the faster train when two trains cross.
• Mixing time in seconds with speed in km/h.
• Missing that a man standing is treated as a pole, but a moving man changes the relative speed.

How to Practice These 30 Questions

1. Memorise the km/h to m/s conversion and the common pairs (36 = 10, 54 = 15, 72 = 20, 90 = 25).
2. First decide which case the question is (pole, platform or two trains).
3. Solve Set 1 in 6 minutes, Set 2 in 12 minutes and Set 3 in 12 minutes.
4. Draw a small diagram for the two-train questions.
5. Revise your mistakes after one day.

Related Topics to Study Next

• Time, Speed and Distance Questions
• Boats and Streams Questions
• Direction and Distance Questions
• SSC Previous Year Papers

Frequently Asked Questions

What is the formula for a train crossing a pole?

Time = length of the train / speed of the train. The distance covered is just the length of the train.

What is the formula for a train crossing a platform?

Time = (length of the train + length of the platform) / speed of the train.

How do you find the time for two trains to cross each other?

Time = (sum of the lengths) / relative speed. For opposite directions, relative speed is the sum of speeds, and for the same direction it is the difference.

How do you convert km/h into m/s?

Multiply the speed in km/h by 5/18. To convert m/s into km/h, multiply by 18/5.

Why do we use relative speed in train questions?

When both objects are moving, the time of crossing depends on how fast one object moves with respect to the other. That speed is the relative speed.

How many train questions come in SSC exams?

Generally one or two questions on trains come in each shift of SSC CGL, CHSL and MTS.

What happens when a train crosses a man walking?

Treat the man as a moving object. Use relative speed (sum for opposite direction, difference for the same direction) and the length of the train as the distance.

How do I solve questions where the length is unknown?

Assume the length as L, form two equations from the given times and solve. Platform questions usually give two equations of the form (L + x)/t = speed.

What are some useful speed conversions?

36 km/h = 10 m/s, 54 km/h = 15 m/s, 72 km/h = 20 m/s and 90 km/h = 25 m/s. Learning these saves time.

How should I prepare train problems for SSC exams?

Learn the three cases, practise unit conversion, solve one set daily and practise mixed TSD questions.