Quiz: Train Crossing Problems
This quiz follows Lesson 5: Problems on Trains: Crossing Poles and Platforms from the course Time, Speed & Distance: Core Concepts for Competitive Exams.
In this lesson you learned how to handle trains crossing stationary objects such as poles, platforms, bridges and tunnels. The key ideas are:
- Crossing a pole: the train covers a distance equal to its own length.
- Crossing a platform or bridge: the train covers a distance equal to its length plus the platform length.
- Relative speed with a stationary object: the train’s own speed is used, since the object does not move.
- Time formula: ##\text{Time} = \dfrac{\text{Total Distance}}{\text{Speed}}##, with careful unit conversion (##\text{km/h} \times \dfrac{5}{18} = \text{m/s}##).
Work through all 20 questions carefully. Each explanation shows the reasoning step by step, so you can check your method as well as your answer.
Q1. A train 150 m long crosses a pole in 10 seconds. What is the speed of the train in m/s?
When a train crosses a pole, the distance covered equals the train's length. ##Speed = \dfrac{150}{10} = 15## m/s.
Q2. A train 200 m long crosses a pole in 8 seconds. What is its speed in km/h?
##Speed = \dfrac{200}{8} = 25## m/s. Converting: ##25 \times \dfrac{18}{5} = 90## km/h.
Q3. A train 120 m long is running at 54 km/h. How long does it take to cross a pole?
##Speed = 54 \times \dfrac{5}{18} = 15## m/s. ##Time = \dfrac{120}{15} = 8## s.
Q4. A train 180 m long crosses a platform 120 m long in 20 seconds. What is the speed of the train?
Total ##distance = 180 + 120 = 300## m. ##Speed = \dfrac{300}{20} = 15## m/s.
Q5. A train 250 m long crosses a platform 350 m long in 30 seconds. What is its speed in km/h?
Total ##distance = 250 + 350 = 600## m. ##Speed = \dfrac{600}{30} = 20## ##m / s = 20 \times \dfrac{18}{5} = 72## km/h.
Q6. A train 100 m long is running at 36 km/h. How long does it take to cross a platform 200 m long?
##Speed = 36 \times \dfrac{5}{18} = 10## m/s. Total ##distance = 100 + 200 = 300## m. ##Time = \dfrac{300}{10} = 30## s.
Q7. When a train crosses a stationary pole, the distance it travels is equal to:
A pole has negligible length, so the train must move forward by exactly its own length to completely pass it.
Q8. When a train crosses a platform, the total distance covered equals:
The front of the train must travel the platform length plus the train's own length so that the rear also clears the platform.
Q9. A train 160 m long crosses a pole in 16 seconds. How long will it take to cross a platform 240 m long?
##Speed = \dfrac{160}{16} = 10## m/s. For the platform, ##distance = 160 + 240 = 400## m. ##Time = \dfrac{400}{10} = 40## s.
Q10. A train 300 m long crosses a pole in 15 seconds. What is the length of a platform it crosses in 25 seconds?
##Speed = \dfrac{300}{15} = 20## m/s. In 25 s the train covers ##20 \times 25 = 500## m. Platform ##length = 500 - 300 = 200## m.
Q11. A train running at 72 km/h crosses a pole in 9 seconds. What is the length of the train?
##Speed = 72 \times \dfrac{5}{18} = 20## m/s. ##Length = 20 \times 9 = 180## m.
Q12. A train running at 90 km/h crosses a platform 250 m long in 18 seconds. What is the length of the train?
##Speed = 90 \times \dfrac{5}{18} = 25## m/s. Total ##distance = 25 \times 18 = 450## m. Train ##length = 450 - 250 = 200## m.
Q13. A train 240 m long crosses a bridge in 24 seconds at 54 km/h. What is the length of the bridge?
##Speed = 54 \times \dfrac{5}{18} = 15## m/s. Total ##distance = 15 \times 24 = 360## m. Bridge ##length = 360 - 240 = 120## m.
Q14. Two trains of the same length cross a pole in 10 s and 15 s respectively. What is the ratio of their speeds?
For equal lengths, speed is inversely proportional to time. Ratio of ##speeds = \dfrac{1}{10} : \dfrac{1}{15} = 3 : 2##.
Q15. A train takes 12 seconds to cross a pole and 20 seconds to cross a platform 160 m long. What is the length of the train?
Let length be ##L## and speed ##v##. Then ##L = 12v## and ##L + 160 = 20v##. Subtracting: ##160 = 8v##, so ##v = 20## m/s and ##L = 240## m.
Q16. A train 150 m long crosses a pole in 10 seconds. How long will it take to cross a bridge 300 m long?
##Speed = \dfrac{150}{10} = 15## m/s. Bridge ##distance = 150 + 300 = 450## m. ##Time = \dfrac{450}{15} = 30## s.
Q17. To convert a speed from km/h to m/s, you should:
Since 1 ##km = 1000## m and 1 ##h = 3600## s, ##1## ##km / h = \dfrac{1000}{3600} = \dfrac{5}{18}## m/s.
Q18. A train 400 m long is running at 108 km/h. How long does it take to cross a platform 500 m long?
##Speed = 108 \times \dfrac{5}{18} = 30## m/s. Total ##distance = 400 + 500 = 900## m. ##Time = \dfrac{900}{30} = 30## s.
Q19. A train crosses a pole in 6 seconds and a platform 180 m long in 15 seconds. What is the speed of the train?
Let length be ##L## and speed ##v##. Then ##L = 6v## and ##L + 180 = 15v##. Subtracting: ##180 = 9v##, so ##v = 20## m/s.
Q20. A train 200 m long crosses a platform in 30 seconds at 72 km/h. What is the length of the platform?
##Speed = 72 \times \dfrac{5}{18} = 20## m/s. Total ##distance = 20 \times 30 = 600## m. Platform ##length = 600 - 200 = 400## m.