Aptitude :: Problems on Trains

Practice :: Problems on Trains - General Questions
Problems on Trains - General Questions

Page Title 11. A train 200 m long is running at a speed of 80 km/h. In what time will it cross a person traveling in the opposite direction of the train at 10 km/h?
10 seconds
8 seconds
11 seconds
9 seconds
Answer: option B

Time = Distance covered/Speed

so we will find the relative speed of the train. They are moving in the opposite direction, so the relative speed = (speed of train + speed of man)

∵ Relative Speed: (80+10) = 90 km/hr

∵ Relative Speed in m/s= 90 x 5/18 = 450/18 = 225/9 m/s

Distance covered to cross the man = length of the train (200 meters)

⟹ Time = 200 x 9/225

⟹ Time = 1800/225 = 8 seconds.



12. At a speed of 72 kmph A goods train is running and crosses a platform 250 m long in 26 seconds. What is the length of the freight train?
273 m
263 m
260 m
270 m
Answer: option D

Speed = (72 x 5/18) m/sec. = 20 m/s

Time = 26 sec.

∵ Let the length of the train be x metres

Then, x + 250/26 = 20

⟹ x + 250 = 520

⟹ x = 270.



13. A train with a speed of 108 km/h crosses a platform in 18 seconds and a person standing on the platform in 10 seconds. Find the length of the platform.
240 meters
247 meters
250 meters
245 meters
Answer: option A

Speed of train in m/s= 108 x 5/18 = 30 m/s

Length of the train = Speed x Time (time taken to cross the man)

= 30 x 10 = 300 meters

Now, the time taken to cross the platform is = Total distance covered/speed of train

Total distance covered = length of train + length of platform

Let the length of platform is X then the total distance = 300 + X

Speed of train = 30 m/s

Time = Distance/speed

⟹ 18 = 300 + X/30

⟹ 540 = 300 + X

⟹ 240 = X or X=240 meters



14. Two trains, each 100 m long, running in opposite directions, cross each other in 8 seconds. If one is moving at twice the speed of the other, then the speed of the faster train is:
65 km/hr
70 km/hr
60 km/hr
63 km/hr
Answer: option C

Let the speed of the slower train be x m/sec.

Then, speed of the faster train = 2x m/sec.

∵ Relative speed = (x + 2x) m/sec = 3x m/sec.

⟹ 100 + 100/8 = 3X

⟹ 24x = 200

⟹ x = 25/3

∵ So, speed of the faster train = 50/3 m/s

= (50/3 x 18/5) km/hr

= 60 km/hr.



15. A train moving at a speed of 108 km/h crosses a platform in 30 seconds. Then it crosses a man running at 12 km/h in the same direction of the train in 9 seconds. What is the length of the train and the platform?
252 & 647
250 & 645
240 & 660
245 & 640
Answer: option C

Let the length of train X meters and length of platform Y meters

Relative Speed of train relative to man = 108 − 12 = 96 km/hr

Relative Speed in m/sec = 96 x 5/18 = 480/18 = 80/3

The distance covered by train to cross the man is equal to its length. So, it is = X meters

∵ So, X = Relative Speed x Time (time taken to cross the man)

⟹ (80/3 x 9) = 240 meters (length of train)

∵ Speed of train in m/s = 108 x 5/18

∵ Time taken to cross the platform = Distance covered (length of train + length of platform)/speed of train

⟹ So, 30 = 240 + Y /30

⟹ 900 = 240 + y

⟹ Y= 900 − 240 = 660 meters (length of platform)




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