Problems on Trains
Problems on Trains
1
A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?  

View Answer
Answer: Option D
Explanation:
Speed=  60 x  5  m/sec  =  50  m/sec.  
18  3 
Length of the train = (Speed x Time) =  50  x 9  m = 150 m.  
3 
2.
A 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:  

View Answer
Answer: Option B
Explanation:
Speed of the train relative to man =  125  m/sec  
10 
=  25  m/sec.  
2 
=  25  x  18  km/hr  
2  5 
= 45 km/hr.
Let the speed of the train be x km/hr. Then, relative speed = (x – 5) km/hr.
x – 5 = 45 x = 50 km/hr.
3.
The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:  

View Answer
Answer: Option C
Explanation:
Speed =  45 x  5  m/sec  =  25  m/sec.  
18  2 
Time = 30 sec.
Let the length of bridge be x metres.
Then,  130 + x  =  25 
30  2 
2(130 + x) = 750
x = 245 m.
4.
View Answer
Answer: Option B
Explanation:
Let the speeds of the two trains be x m/sec and y m/sec respectively.
Then, length of the first train = 27x metres,
and length of the second train = 17y metres.
27x + 17y  = 23  
x+ y 
27x + 17y = 23x + 23y
4x = 6y
x  =  3  .  
y  2 
5.
A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?  

View Answer
Answer: Option B
Explanation:
Speed =  54 x  5  m/sec = 15 m/sec.  
18 
Length of the train = (15 x 20)m = 300 m.
Let the length of the platform be x metres.
Then,  x + 300  = 15 
36 
x + 300 = 540
x = 240 m.
6.
A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?  

View Answer
Answer: Option B
Explanation:
Speed =  240  m/sec = 10 m/sec.  
24 
Required time =  240 + 650  sec = 89 sec.  
10 
7.
Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is:  

View Answer
Answer: Option A
Explanation:
Let the length of each train be x metres.
Then, distance covered = 2x metres.
Relative speed = (46 – 36) km/hr
=  10 x  5  m/sec  
18 
=  25  m/sec  
9 
2x  =  25  
36  9 
2x = 100
x = 50.
8.
A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?  

View Answer
Answer: Option A
Explanation:
Formula for converting from km/hr to m/s: X km/hr =  X x  5  m/s.  
18 
Therefore, Speed =  45 x  5  m/sec  =  25  m/sec.  
18  2 
Total distance to be covered = (360 + 140) m = 500 m.
Formula for finding Time =  Distance  
Speed 
Required time =  500 x 2  sec  = 40 sec.  
25 
9.
Two 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:  

View Answer
Answer: Option C
Explanation:
Relative speed = (60+ 90) km/hr
=  150 x  5  m/sec  
18 
=  125  m/sec.  
3 
Distance covered = (1.10 + 0.9) km = 2 km = 2000 m.
Required time =  2000 x  3  sec = 48 sec.  
125 
10.
A 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?  

View Answer
Answer: Option C
Explanation:
Speed of train relative to jogger = (45 – 9) km/hr = 36 km/hr.
=  36 x  5  m/sec  
18 
= 10 m/sec.
Distance to be covered = (240 + 120) m = 360 m.
Time taken =  360  sec  = 36 sec.  
10 
11
A 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?  

View Answer
Answer: Option A
Explanation:
Relative speed = (120 + 80) km/hr
=  200 x  5  m/sec  
18 
=  500  m/sec.  
9 
Let the length of the other train be x metres.
Then,  x + 270  =  500 
9  9 
x + 270 = 500
x = 230.
12.
A 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?  

View Answer
Answer: Option D
Explanation:
Speed =  72 x  5  m/sec  = 20 m/sec.  
18 
Time = 26 sec.
Let the length of the train be x metres.
Then,  x + 250  = 20 
26 
x + 250 = 520
x = 270.
13.
Two 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:  

View Answer
Answer: Option C
Explanation:
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)  = 3x  
8 
24x = 200
x =  25  . 
3 
So, speed of the faster train =  50  m/sec 
3 
=  50  x  18  km/hr  
3  5 
= 60 km/hr.
14.
Two 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:  

View Answer
Answer: Option D
Explanation:
Relative speed = (60 + 40) km/hr =  100 x  5  m/sec  =  250  m/sec.  
18  9 
Distance covered in crossing each other = (140 + 160) m = 300 m.
Required time =  300 x  9  sec  =  54  sec = 10.8 sec.  
250  5 
15.
A 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?  

View Answer
Answer: Option B
Explanation:
Speed of train relative to man = (60 + 6) km/hr = 66 km/hr.
=  66 x  5  m/sec  
18 
=  55  m/sec.  
3 
Time taken to pass the man =  110 x  3  sec = 6 sec.  
55 
16.
A train travelling at a speed of 75 mph enters a tunnel 3 miles long. The train is mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?  

View Answer
Answer: Option B
Explanation:
Total distance covered 



Time taken 






= 3 min. 
17.
A 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:  

View Answer
Answer: Option C
Explanation:
Speed =  78 x  5  m/sec  =  65  m/sec.  
18  3 
Time = 1 minute = 60 seconds.
Let the length of the tunnel be x metres.
Then,  800 + x  =  65  
60  3 
3(800 + x) = 3900
x = 500.
18.
A 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?  

View Answer
Answer: Option B
Explanation:
Speed =  300  m/sec =  50  m/sec.  
18  3 
Let the length of the platform be x metres.
Then,  x + 300  =  50  
39  3 
3(x + 300) = 1950
x = 350 m.
19.
A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:  

View Answer
Answer: Option B
Explanation:
Let the length of the train be x metres and its speed by y m/sec.
Then,  x  = 15 y =  x  . 
y  15 
x + 100  =  x  
25  15 
15(x + 100) = 25x
15x + 1500 = 25x
1500 = 10x
x = 150 m.
20.
A 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?  

View Answer
Answer: Option D
Explanation:
Let the length of the train be x metres and its speed by y m/sec.
Then,  x  = 8 x = 8y 
y 
Now,  x + 264  = y 
20 
8y + 264 = 20y
y = 22.
Speed = 22 m/sec =  22 x  18  km/hr = 79.2 km/hr.  
5 
21
How 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?  

View Answer
Answer: Option B
Explanation:
Speed of the train relative to man  = (63 – 3) km/hr  
= 60 km/hr  




Time taken to pass the man 


= 30 sec. 
22.
Two 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.  

View Answer
Answer: Option B
Explanation:
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 =  500 x  6  = 24 sec.  
125 
23.
Two 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:  

View Answer
Answer: Option C
Explanation:
Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x =  (120 + 120) 
12 
2x = 20
x = 10.
Speed of each train = 10 m/sec =  10 x  18  km/hr = 36 km/hr.  
5 
24.
Two 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?  

View Answer
Answer: Option B
Explanation:
Speed of the first train =  120  m/sec = 12 m/sec.  
10 
Speed of the second train =  120  m/sec = 8 m/sec.  
15 
Relative speed = (12 + 8) = 20 m/sec.
Required time =  (120 + 120)  sec = 12 sec.  
20 
25.
A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the second train is:  

View Answer
Answer: Option D
Explanation:
Let the speed of the second train be x km/hr.
Relative speed  = (x + 50) km/hr  



Distance covered = (108 + 112) = 220 m.
220  = 6  

250 + 5x = 660
x = 82 km/hr.