Quantitative Aptitude

Problems on Trains: Practice Questions with Answers

14 practice questions on Problems on Trains, with answers; most also have an explanation or a worked solution. Try each one before you open its answer.

Read the lesson on this topic →

1. Q.1

   Two trains, 120 m and 180 m long, run on parallel tracks in the SAME direction at 72 km/hr and 54 km/hr. Find the time for the faster train to completely cross the slower one.

   Show answer

   Answer: 60 seconds

   Solution:

   1. Same direction, so relative speed = difference of speeds = 72 − 54 = 18 km/hr.
   2. Convert to m/s: 18 × 5/18 = 5 m/s.
   3. Distance to cover = sum of both lengths = 120 + 180 = 300 m.
   4. Time = Distance / Speed = 300 / 5 = 60 seconds.

   Report this question

2. Q.2

   A train 150 m long running at 70 km/hr crosses a man walking in the SAME direction at 10 km/hr. Find the time taken to cross him.

   Show answer

   Answer: 9 seconds

   Solution:

   1. Same direction, so relative speed = 70 − 10 = 60 km/hr.
   2. Convert to m/s: 60 × 5/18 = 50/3 m/s.
   3. Time = Distance / Speed = 150 / (50/3) = 150 × 3/50 = 9 seconds.

   Report this question

3. Q.3

   A train 180 m long is running at 54 km/hr. How long will it take to cross a man standing on the platform?

   Show answer

   Answer: 12 seconds

   Solution:

   1. Convert speed to m/s: 54 × 5/18 = 15 m/s.
   2. Crossing a man (a point) means covering a distance equal to the train’s own length: 180 m.
   3. Time = Distance / Speed = 180 / 15 = 12 seconds.

   Report this question

4. Q.4

   Two trains, 140 m and 160 m long, run on parallel tracks in OPPOSITE directions at 60 km/hr and 48 km/hr. Find the time for them to cross each other.

   Show answer

   Answer: 10 seconds

   Solution:

   1. Opposite directions, so relative speed = sum of speeds = 60 + 48 = 108 km/hr.
   2. Convert to m/s: 108 × 5/18 = 30 m/s.
   3. Distance to cover = sum of both lengths = 140 + 160 = 300 m.
   4. Time = Distance / Speed = 300 / 30 = 10 seconds.

   Report this question

5. Q.5

   Two trains start at the same time from stations A and B towards each other. After crossing each other, they take 4 hours and 9 hours respectively to reach stations B and A. Find the ratio of their speeds.

   Show answer

   Answer: 3 : 2

   Solution:

   1. Using the shortcut: speed of train from A / speed of train from B = √(b/a), where a = 4 (A-train's remaining time) and b = 9 (B-train's remaining time).
   2. = √(9/4) = 3/2.
   3. So the speeds are in the ratio 3 : 2 — the train from A is faster, consistent with it needing less time to finish its remaining distance.

   Report this question

6. Q.6

   A train 200 m long is running at 66 km/hr. It crosses a man walking in the OPPOSITE direction at 6 km/hr. Find the time taken to cross him.

   Show answer

   Answer: 10 seconds

   Solution:

   1. Opposite directions, so relative speed = 66 + 6 = 72 km/hr.
   2. Convert to m/s: 72 × 5/18 = 20 m/s.
   3. Distance to cover is just the train's length (the man has no length): 200 m. Time = 200 / 20 = 10 seconds.

   Report this question

7. Q.7

   A train 150 m long running at 72 km/hr crosses a platform in 25 seconds. Find the length of the platform.

   Show answer

   Answer: 350 m

   Solution:

   1. Convert speed to m/s: 72 × 5/18 = 20 m/s.
   2. Distance covered in 25 seconds = 20 × 25 = 500 m.
   3. This distance is the train’s length plus the platform’s length, so platform length = 500 − 150 = 350 m.

   Report this question

8. Q.8

   A train crosses a man standing on a platform in 10 seconds, and crosses the entire 300 m long platform in 25 seconds. Find the length and speed of the train.

   Show answer

   Answer: Length = 200 m, Speed = 20 m/s. Let speed = s; train length = 10s; 10s + 300 = 25s gives s = 20.

   Report this question

9. Q.9

   Two trains start simultaneously from stations P and Q towards each other. After crossing, they take 16 hours and 9 hours respectively to reach Q and P. Find the ratio of their speeds.

   Show answer

   Answer: 3 : 4. √(9/16) = 3/4.

   Report this question

10. Q.10

    Two trains, 100 m and 140 m long, run on parallel tracks in the same direction at 63 km/hr and 45 km/hr. Find the time for the faster train to completely cross the slower one.

    Show answer

    Answer: 48 seconds

    Report this question

11. Q.11

    A train 180 m long is running at 50 km/hr. It crosses a man walking in the opposite direction at 4 km/hr. Find the time taken.

    Show answer

    Answer: 12 seconds. Relative speed = 54 km/hr = 15 m/s; 180/15.

    Report this question

12. Q.12

    A train 250 m long running at 108 km/hr crosses a platform in 30 seconds. Find the length of the platform.

    Show answer

    Answer: 650 m

    Report this question

13. Q.13

    A train 120 m long running at 56 km/hr crosses a man walking in the same direction at 8 km/hr. Find the time taken.

    Show answer

    Answer: 9 seconds. Relative speed = 48 km/hr = 40/3 m/s; 120 ÷ (40/3).

    Report this question

14. Q.14

    A train 200 m long is running at 90 km/hr. How long will it take to cross a lamp post?

    Show answer

    Answer: 8 seconds

    Report this question

Practise this topic →