We cover all the topics and concepts of Aptitude Problems on trains like two trains are moving in opposite directions, calculate train speed, calculate distance, etc.
Rules on Problem On Trains
Rule 1: When two trains are moving in opposite directions, then relative speed will be the addition of their individual speeds.
Rule 2: When two trains are moving in same direction, then relative speed will be the subtraction of their individual speeds.
Rule 3: On passing a platform by a certain train the net distance traveled is the sum of length of train and the length of platform both.
Rule 4: When a train passes through a pole or person standing, net distance traveled to pass is the length of the train
Problems on Trains Formulas
 x
 y
 Speed = distance/time
 Velocity = displacement/time
 Time taken by a train x meters long to pass a pole or standing man or a post = Time taken by the train to travel x meters.
 Time taken by a train x meters long to pass an object of length y meters = Time taken by the train to travel (x + y) metres.
 Suppose two trains or two objects are moving in the same direction at v1 m/s and v2 m/s where v 1 > v 2, then their relative speed = (v 1 v 2) m/s
 Suppose two trains or two objects are moving in opposite directions at v 1 m/s and v 2 m/s , then their relative speed = (v 1+ v 2) m/s
 Assume two trains of length x metres and y metres are moving in opposite directions at v 1 m/s and v 2 m/s, Then the time taken by the trains to cross each other = (x+y) / (v 1+v 2) seconds
 Assume two trains of length x metres and y metres are moving in the same direction at at v 1 m/s and v 2 m/s where v 1 > v 2, Then The time taken by the faster train to cross the slower train = (x+y) / (v 1v 2) seconds.
 Assume that two trains (objects) start from two points P and Q towards each other at the same time and after crossing they take p and q seconds to reach Q and P respectively. Then, A's speed: B's speed =
Problems on Trains Aptitude Questions from Previous Year Exams
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Question 1 of 33
1. Question
1 pointsTwo trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train?
Correct
Relative speed = (40  20) km/hr
Length of faster train =
Incorrect
Relative speed = (40  20) km/hr
Length of faster train =

Question 2 of 33
2. Question
1 pointsTwo trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:
Correct
Let the speed of each train beÂ xÂ m/sec.
Then, relative speed of the two trains = 2xÂ m/sec.
So 2x =
2xÂ = 20
xÂ = 10.
Speed of each train = 10 m/sec = km/hr = 36 km/hr
Incorrect
Let the speed of each train beÂ xÂ m/sec.
Then, relative speed of the two trains = 2xÂ m/sec.
So 2x =
2xÂ = 20
xÂ = 10.
Speed of each train = 10 m/sec = km/hr = 36 km/hr

Question 3 of 33
3. Question
1 pointsA train takes 18 seconds to pass completely through a station 162 m long and 15 seconds through another station 120 m long. The length of the train is
Correct
Let the length of the train be x meters. =
=
= 15( x+162)
= 18(x+120)
x= 90.
Incorrect
Let the length of the train be x meters. =
=
= 15( x+162)
= 18(x+120)
x= 90.

Question 4 of 33
4. Question
1 pointsA 300 metre long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
Correct
Speed =Â Â m/sec = 50 m/sec.
Let the length of the platform be x meters. Then,
=> 3(x + 300) = 1950
=> x = 350 m.
Incorrect
Speed =Â Â m/sec = 50 m/sec.
Let the length of the platform be x meters. Then,
=> 3(x + 300) = 1950
=> x = 350 m.

Question 5 of 33
5. Question
1 pointsTwo trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?
Correct
Speed of the first train = m/sec = 12 m/sec.
Speed of the second train = m/sec = 8 m/sec.
Relative speed = (12 + 8) = 20 m/sec.
Therefore Required time = sec = 12 sec.
Incorrect
Speed of the first train = m/sec = 12 m/sec.
Speed of the second train = m/sec = 8 m/sec.
Relative speed = (12 + 8) = 20 m/sec.
Therefore Required time = sec = 12 sec.

Question 6 of 33
6. Question
1 pointsA train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:
Correct
Incorrect
Let the length of the train beÂ xÂ metres and its speed byÂ yÂ m/sec
Â 9yÂ  5 =Â xÂ and 10(9yÂ  10) = 9x
Â 9yÂ Â xÂ = 5 and 90yÂ  9xÂ = 100.
On solving, we get:Â xÂ = 50.
Â Length of the train is 50 m.

Question 7 of 33
7. Question
1 pointsA train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
Correct
Incorrect
Speed of the train relative to man =
Let the speed of the train beÂ xÂ km/hr. Then, relative speed = (xÂ  5) km/hr.
xÂ  5 = 45
xÂ = 50 km/hr. 
Question 8 of 33
8. Question
1 pointsA train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
Correct
Incorrect
Length of the train = (Speed x Time)

Question 9 of 33
9. Question
1 pointsA 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
Correct
Relative speed = (120 + 80) km/hr
Let the length of the other train be x metres.
Then,
x+ 270 = 500
x = 230.
Incorrect
Relative speed = (120 + 80) km/hr
Let the length of the other train be x metres.
Then,
x+ 270 = 500
x = 230.

Question 10 of 33
10. Question
1 pointsTwo trains, each 100 m long, moving in opposite directions, cross each other in 8 seconds. If one is moving twice as fast the other, then the speed of the faster train is:
Correct
Incorrect
Let the speed of the slower train beÂ xÂ m/sec.
Then, speed of the faster train = 2xÂ m/sec.
Relative speed = (xÂ + 2x) m/sec = 3xÂ m/sec.
24xÂ = 200
So, the speed of the faster train=

Question 11 of 33
11. Question
1 pointsTwo trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?
Correct
Relative speed = (12 + 8) =20 m/sec.
Required time =
Incorrect
Relative speed = (12 + 8) =20 m/sec.
Required time =

Question 12 of 33
12. Question
1 pointsA train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:
Correct
Incorrect
Let the length of the train beÂ xÂ metres and its speed byÂ yÂ m/sec.
Then,
15(xÂ + 100) = 25x
15xÂ + 1500 = 25x
1500 = 10x
xÂ = 150 m.

Question 13 of 33
13. Question
1 pointsA train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?
Correct
Incorrect

Question 14 of 33
14. Question
1 pointsA goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?
Correct
Incorrect
Time = 26 sec.
Let the length of the train beÂ xÂ metres.
xÂ + 250 = 520
xÂ = 270.

Question 15 of 33
15. Question
1 pointsA jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?
Correct
Speed of train relative to jogger = (45  9) km/hr =36 km/hr.
Distance to be covered = (240 + 120) m = 360 m.
Incorrect
Speed of train relative to jogger = (45  9) km/hr =36 km/hr.
Distance to be covered = (240 + 120) m = 360 m.

Question 16 of 33
16. Question
1 pointsTwo stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
Correct
Incorrect
Suppose they meetÂ xÂ hours after 7 a.m.
Distance covered by A inÂ xÂ hours = 20xÂ km.
Distance covered by B in (xÂ  1) hours = 25(xÂ  1) km.
20xÂ + 25(xÂ  1) = 110
Â 45xÂ = 135
Â xÂ = 3.
So, they meet at 10 a.m.

Question 17 of 33
17. Question
1 pointsA train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Correct
Incorrect
Formula for converting from km/hr to m/s: Â Â XÂ km/hr =
Total distance to be covered =(360 + 140) m=500 m.
Formula for finding Time =

Question 18 of 33
18. Question
1 pointsHow many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Correct
Incorrect
Speed of the train relative to manÂ = (63  3) km/hr= 60 km/hr
Time taken to pass the man=

Question 19 of 33
19. Question
1 pointsTwo goods train each 500 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one.
Correct
Incorrect
Relative speed =(45 + 30) km/hr
We have to find the time taken by the slower train to pass the DRIVER of the faster train and not the complete train.
So, distance covered = Length of the slower train.
Therefore, Distance covered = 500 m.
Required time =

Question 20 of 33
20. Question
1 pointsTwo trains are moving in opposite directions @ 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is:
Correct
Relative speed = (60+ 90) km/hr
Distance covered = (1.10 + 0.9) km = 2 km = 2000 m.
Required time =
Incorrect
Relative speed = (60+ 90) km/hr
Distance covered = (1.10 + 0.9) km = 2 km = 2000 m.
Required time =

Question 21 of 33
21. Question
1 pointsA train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is:
Correct
Incorrect
Speed=
Time = 1 minute = 60 seconds.
Let the length of the tunnel beÂ xÂ metres.
Â 3(800 +Â x) = 3900
Â xÂ = 500.

Question 22 of 33
22. Question
1 pointsThe length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
Correct
Time = 30 sec.
Let the length of bridge beÂ xÂ metres.
2(130 +Â x) = 750
xÂ = 245 m.
Incorrect
Time = 30 sec.
Let the length of bridge beÂ xÂ metres.
2(130 +Â x) = 750
xÂ = 245 m.

Question 23 of 33
23. Question
1 pointsA train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
Correct
Speed= m/s = m/s.
Length of the train = (Speed Time) = m = 150 m
Incorrect
Speed= m/s = m/s.
Length of the train = (Speed Time) = m = 150 m

Question 24 of 33
24. Question
1 pointsA train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?
Correct
speed = m/sec = 10 m/sec.
Required time = sec = 89 sec
Incorrect
speed = m/sec = 10 m/sec.
Required time = sec = 89 sec

Question 25 of 33
25. Question
1 pointsHow many seconds will a 500 metre long train take to cross a man walking with a speed of 3 krn/hr in the direction of the moving train if the speed of the train is 63 km/hr ?
Correct
Incorrect
Speed of train relatively to man = ( 63  3)km/hr = 60 km /hr
= m/sec
= m/sec
Time taken to pass the man = sec = 30 sec.

Question 26 of 33
26. Question
1 pointsTwo trains 200 m and 150 m long are running on parallel rails at the rate of 40 kmph and 45 kmph respectively. In how much time will they cross each other, if they are running in the same direction ?
Correct
Relative Speed = (45  40 ) Kmph = 5 kmph
= m/sec
=
Time taken = = 252 sec
Incorrect
Relative Speed = (45  40 ) Kmph = 5 kmph
= m/sec
=
Time taken = = 252 sec

Question 27 of 33
27. Question
1 pointsTwo, trains, one from Howrah to Delhi and the other fromÂ DelhiÂ to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is
Correct
Let us name the trains as A and B. Then,
(A's speed) : (B's speed) = = 4 : 3.
Incorrect
Let us name the trains as A and B. Then,
(A's speed) : (B's speed) = = 4 : 3.

Question 28 of 33
28. Question
1 pointsA train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?
Correct
Let the length of train be x meters and its speed be y m/sec
then, = 8 x = 8y
Now = y
8y + 264 = 20y
y = 22
Speed = 22 m/sec = km/h = 79.2 km/h
Incorrect
Let the length of train be x meters and its speed be y m/sec
then, = 8 x = 8y
Now = y
8y + 264 = 20y
y = 22
Speed = 22 m/sec = km/h = 79.2 km/h

Question 29 of 33
29. Question
1 pointsTwo trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other is
Correct
Relative speed = (60 + 40)km/h = m/sec =
Distance covered in crossing each other = (140 + 160) m = 300 m.
Required time = sec = sec= 10.8 sec Incorrect
Relative speed = (60 + 40)km/h = m/sec =
Distance covered in crossing each other = (140 + 160) m = 300 m.
Required time = sec = sec= 10.8 sec" />
Incorrect
Relative speed = (60 + 40)km/h = m/sec =
Distance covered in crossing each other = (140 + 160) m = 300 m.
Required time = sec = sec= 10.8 sec

Question 30 of 33
30. Question
1 pointsA train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?
Correct
4.5km/h = m/sec = m/sec = 1.25Â m/sec
5.4km/h = Â m/sec = m/sec = \times \times \left ( 22.5\times\frac{18}{5}\right ) Incorrect
4.5km/h = m/sec = m/sec = 1.25 m/sec
5.4km/h = m/sec = m/sec = \times \times \left ( 22.5\times\frac{18}{5}\right )" /> m/sec = m/sec = 1.25 m/sec
5.4km/h = m/sec = m/sec = \times \times \left ( 22.5\times\frac{18}{5}\right ) km/h = 81 km/h

Question 31 of 33
31. Question
1 pointsTwo trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
Correct
Let the speeds of the two trains beÂ xÂ m/sec and y m/sec respectively.
Then, length of the first train = 27Â xÂ metres,
and length of the second train = 17Â yÂ metres.
27xÂ + 17yÂ = 23xÂ + 23y
4xÂ = 6y
Incorrect
Let the speeds of the two trains beÂ xÂ m/sec and y m/sec respectively.
Then, length of the first train = 27Â xÂ metres,
and length of the second train = 17Â yÂ metres.
27xÂ + 17yÂ = 23xÂ + 23y
4xÂ = 6y

Question 32 of 33
32. Question
1 pointsA train 110 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
Correct
Incorrect
Speed of train relative to man = (60 + 6) km/hr = 66 km/hr.

Question 33 of 33
33. Question
1 pointsTwo, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:
Correct
Incorrect
Let us name the trains as A and B. Then,
(A's speed) : (B's speed) =
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