Problems on Trains Notes for SSC Exams

Problems on Trains is a regular chapter in SSC Quantitative Aptitude, and one question is asked from it in most exams. It uses the speed-distance-time formula along with the length of the train. These problems on trains notes for SSC explain every crossing case with formulas, solved examples and practice questions.

Key Idea

• When a train crosses an object, it covers a distance equal to its own length plus the length of the object.
• A pole, a tree or a standing man has no length, so the train covers only its own length.
• Convert speeds from km/h into m/s (multiply by 5/18) when lengths are in metres.
• Speed = Distance / Time in all cases.

Formulas for Different Crossing Cases

Useful Speed Conversions

Special Cases

• If two trains of equal length cross each other in a time t, then the time taken in each case depends on the sum of lengths.
• If two trains start from two stations towards each other and meet, the ratio of the distances they cover equals the ratio of their speeds.
• After meeting, if the trains take t1 and t2 hours to reach the other's starting point, the ratio of the speeds = square root of t2 : square root of t1.

Solved Examples

Example 1: A train 150 m long runs at 54 km/h. How long does it take to cross a pole?
Solution: Speed = 54 x 5/18 = 15 m/s. Time = 150 / 15 = 10 seconds.

Example 2: A train 200 m long crosses a 300 m long platform in 25 seconds. Find its speed.
Solution: Distance = 200 + 300 = 500 m. Speed = 500 / 25 = 20 m/s = 72 km/h.

Example 3: Two trains of lengths 120 m and 130 m run in opposite directions at 60 km/h and 40 km/h. In what time do they cross each other?
Solution: Relative speed = 100 km/h = 100 x 5/18 = 250/9 m/s. Time = 250 / (250/9) = 9 seconds.

Example 4: Two trains of lengths 100 m and 150 m run in the same direction at 54 km/h and 36 km/h. How long does the faster train take to overtake the slower one?
Solution: Relative speed = 18 km/h = 5 m/s. Time = 250 / 5 = 50 seconds.

Example 5: A train 180 m long moving at 60 km/h passes a man walking in the same direction at 6 km/h. Find the time.
Solution: Relative speed = 54 km/h = 15 m/s. Time = 180 / 15 = 12 seconds.

Example 6: A train crosses a pole in 12 seconds and a platform of 180 m in 30 seconds. Find the length of the train.
Solution: Extra time for the platform = 18 seconds, which covers 180 m, so speed = 10 m/s. Length = 10 x 12 = 120 m.

Quick Tips to Solve Faster

• Convert the speed into m/s as soon as you see lengths in metres.
• For opposite directions add the speeds, and for the same direction subtract them.
• The length of the object is covered in the extra time taken to cross it.
• A moving man must be included in the relative speed; a standing man is like a pole.
• Memorise 36 km/h = 10 m/s and 72 km/h = 20 m/s.

Common Mistakes to Avoid

• Forgetting to add the length of the platform or the other train.
• Adding the speeds when both trains go in the same direction.
• Using km/h with metres without converting.
• Taking the length of a man or a pole into the distance.
• Dividing by the wrong relative speed in overtaking problems.

Quick Revision Points

• Distance to cross a platform = L + P.
• Opposite direction: relative speed = s1 + s2.
• Same direction: relative speed = s1 - s2.
• km/h to m/s: multiply by 5/18.
• Crossing a pole: distance = length of the train.

Practice Questions With Answers

1. A train 100 m long runs at 36 km/h. How long does it take to cross a pole?
   Answer: 10 seconds (36 km/h = 10 m/s).
2. A train 250 m long running at 72 km/h crosses a 250 m platform. Find the time.
   Answer: 25 seconds (500 / 20).
3. A train at 90 km/h crosses a tunnel of 500 m in 30 seconds. Find the length of the train.
   Answer: 250 m (25 x 30 = 750; 750 - 500).
4. Two trains 150 m and 100 m long run in opposite directions at 54 km/h and 36 km/h. Find the crossing time.
   Answer: 10 seconds (250 / 25).
5. Two trains 200 m and 100 m long run in the same direction at 72 km/h and 36 km/h. Find the overtaking time.
   Answer: 30 seconds (300 / 10).
6. A train 120 m long crosses a standing man in 6 seconds. Find its speed in km/h.
   Answer: 72 km/h (20 m/s).
7. A train 300 m long at 54 km/h crosses a bridge in 40 seconds. Find the length of the bridge.
   Answer: 300 m (600 - 300).
8. A train 110 m long at 60 km/h passes a man running at 6 km/h in the opposite direction. Find the time.
   Answer: 6 seconds (66 km/h = 55/3 m/s).
9. Two trains of 100 m each run in opposite directions at 36 km/h and 54 km/h. Find the crossing time.
   Answer: 8 seconds (200 / 25).
10. A train 160 m long passes a pole in 8 seconds. Find its speed in km/h.
    Answer: 72 km/h (20 m/s).

How to Practise This Chapter

1. Learn the formulas in the table until you can write them without looking.
2. Solve the solved examples again on your own, without reading the solution.
3. Attempt the practice questions above with a timer of 10 minutes.
4. Solve the matching SSC problems on trains practice paper to test yourself in exam style.
5. Check the previous year papers to see how SSC frames this topic.

Related Notes and Practice Papers

• Speed, Distance and Time Notes
• Boats and Streams Notes
• Ratio and Proportion Notes
• Average Notes
• SSC Problems on Trains Practice Paper

Explore More SSC Subjects

SSC exams test many subjects, so connect this topic with the related subjects below:

• Reasoning Notes
• Statistics Notes
• Indian Economy Notes
• English Notes
• General Awareness Notes
• All SSC subjects and notes

Frequently Asked Questions

What are problems on trains?

These are questions in which a train of a given length crosses a pole, a platform, a person or another train, and we find the time, speed or length.

How many questions come from trains in SSC exams?

Usually one question comes from this chapter in SSC CGL and CHSL Tier 1.

What is the distance covered while crossing a platform?

The train covers its own length plus the length of the platform.

What is the formula for two trains moving in opposite directions?

Time = (L1 + L2) / (s1 + s2).

What is the formula for two trains moving in the same direction?

Time = (L1 + L2) / (s1 - s2), where s1 is the speed of the faster train.

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

Multiply the speed in km/h by 5/18.

Why does a pole only count the length of the train?

Because a pole has no length, so the train needs to cover only its own length to cross it.

How should I practise this chapter?

Learn the cases in the table, solve the examples here and then attempt the trains practice paper.