## RRB NTPC - Problems on Trains

• 51. In what time will a train 100 metres long cross an electric pole, if its speed be 144 km/hr?
A.) 4.25 seconds
B.) 5 seconds
C.) 12.5 seconds
D.) 2.5 seconds

Given
Length of the train = 100 m
Speed of the train = 144 km / hr
---> To convertkm/hr to m/sec multiply speed with (5 / 18)
= 144 x (5 / 18) m/sec
= 40 m/sec
Therefore Speed of the train =40 m/sec
Now, Time taken by the train tocross an electric pole =Length of the train/Speed of the train
T = 100 / 40
2.5 sec
The time taken is 2.5 sec.

• 52. Two trains 100 metres and 120 metres long are running in the same direction with the speeds of 72 km/hr and 54 km/hr .In how much time will the first train cross the second?
A.) 45 second
B.) 44.5 second
C.) 44 second
D.) 41.2 second

44 second

• 53. A train is moving at a speed of 132 km/hr .If the length of the train is 110 metres ,how long will it take to cross a railway platform 165 metres long?
A.) 7 sec
B.) 7 1/2 sec
C.) 5 sec
D.) 6 1/2 sec

7 1/2 sec

• 54. A train 100 m long is running at the speed of 30 km/hr.Find the time taken by it to pass a man standing near the railway line:
A.) 12 sec
B.) 10 sec
C.) 8 sec
D.) 5 sec

12 sec

• 55. 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.
A.) 12 sec
B.) 24 sec
C.) 48 sec
D.) 60 sec

Relative speed = (45 + 30) km/hr = ( 75 x 5/18 ) m/sec = (125/6 ) m/sec .
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.
Therefore Required time = ( 500 x 6/125 ) = 24 sec .

• 56. 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?
A.) 25
B.) 30
C.) 40
D.) 45

Given, Length of the train = 500 m
Speed of the man = 3 km/hr
Speed of the train = 63 km/hr
Time taken by the train to cross a man = Length of the train / (speed of the train – speed of the man)
=> Time = 500 m / (63 – 3) km/hr
=> Time = 500 m / 60 km/hr
(to convert 60 km/hr to m/sec)
=> Time = 500 m / [60 × (5/18) m/sec]
=> Time = {500 / [60 × (5/18)]} sec
=> Time = {(500 × 18) / (60 × 5)} sec
=>Time = 30 sec

• 57. 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?
A.) 69.5 km/hr
B.) 70 km/hr
C.) 79.2 km/hr
D.) 79 km/hr

Let the length of the train be x metres and its speed by y m/sec.
Time = Length / Speed of the train
Given,A train moves past a telegraph post in 8 seconds.
Then, x/y = 8
=> x = 8y
Now, the same train moves past a bridge of 264 m long in 20 seconds.
=> (x + 264) / y = 20
Subs x = 8y in the above eqn, we get
=> (8y + 264) = 20y
=> 20y - 8y = 264
=> 12y = 264
=> y = 22.
Therefore Speed = 22 m/sec = ( 22 x 18 /5) km/hr = 79.2 km/hr.

• 58. A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:
A.) 200 m
B.) 150 m
C.) 50 m

Given time taken by train to pass the pole =15 seconds
=> W.K.T: Time = Distance / speed
=> Time = Length of train / speed of train
=> 15 = Length of train/ speed of train
=>speed of train =Length of train /15 ---> eqn(1)
Given, time taken by train to pass the platform of 100 m long =25 seconds
=>Time = (Length of train + Length of the platform) / speed of train
=> 25 = (Length of train + 100) /speed of train
Substituting eqn (1) in the above eqn, we get
=> 25 =(Length of train + 100) / (Length of train /15)
=> 25 × (Length of train /15) =(Length of train + 100)
=> (5 / 3) × Length of train =(Length of train + 100)
=> 5 × Length of train = 3 (Length of train + 100)
=> 5 × Length of train =3 × Length of train + 300
=> 2 × Length of train = 300
=> Length of train = 150 meter.

• 59. 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 :
A.) 500
B.) 540
C.) 360
D.) 130

Given, Length of the train = 800 m
Speed ofthe train = 78 km/hr
= 78 × (5 / 18) m/s
= 390 / 18 m/s
Time to cross the tunnel = 1 min = 60 sec
Formula: Distance = Speed × Time
=> Length of the train + length of the tunnel = Speed of the train × Time to cross the tunnel
=> 800 + length of the tunnel = (390 / 18) × 60
=> 800 + length of the tunnel = 23400 / 18
=> 800 + length of the tunnel = 1300
=> length of the tunnel = 1300 - 800 = 500 m

• 60. A train travelling at a speed of 75 mph enters a tunnel 3 (1/2) miles long. The train is 1/4 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?
A.) 2.5 min
B.) 3 min
C.) 3.2 min
D.) 3.5 min

Total distance covered = ( 7/2 + 1/4 ) miles
= 15/4 miles.
Therefore, Time taken
= ( 15 / 4 x 75 ) hrs
= 1 / 20 hrs
= ( 1/20 x 60 ) min.
= 3 min.

• 61. 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?
A.) 5 sec
B.) 6 sec
C.) 7 sec
D.) 10 sec

Speed of train relative to man = (60 + 6) km/hr = 66 km/hr. = ( 66 x 5 /18 m/sec = (55 / 3 ) m/sec
Therefore, Time taken to pass the man = ( 110 x 3/55 ) sec = 6 sec.

• 62. 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:
A.) 30 km/hr
B.) 45 km/hr
C.) 60 km/hr
D.) 75 km/hr

Given, Length of each train = 100 m
=> Sum of length of two trains = 100 + 100 = 200 m
Time taken by the trains to cross each other = 8 sec.
Let the speed of the slower train be x m/sec.
Then, speed of the faster train = 2x m/sec.
(Since, two trains are moving in opposite direction, Speed can be added)
Relative speed = speed of the slower train +speed of the faster train
= (x + 2x) m/sec
3x m/sec.

W.K.T: Relative speed =Sum of length of two trains /Time taken by the trains to cross each other
=> 3x = (100 + 100) / 8
=> 3x = 200 / 8
=> x = 200/ (8*3) m/sec
=> x = (200 / 24) m/sec
=> x = 8.33m/sec
Speed of faster train
= 2x
= 2 × 8.33
= 16.66 m/sec
---> Converting into km/hr
= 16.66 × (18 /5) km/hr
= 299.88/5 km/hr
= 59.976 km/hr
= 60 km/hr
Therefore,Speed of faster train
=60 km/hr

• 63. 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?
A.) 230 m
B.) 240 m
C.) 260 m
D.) 320 m

Given the length of the first train = 270 metres.
Let the length of the second train be x metres
Relative speed = Speed of first train + Speed of Second Train
= (120 + 80) kmph
= ( 200 x 5/18 ) m/sec
= 1000/ 18 m/sec.
Therefore,Time taken by the first train to cross the another train = Length of two trains / Relative speed
=> 9 = [ 270 + x ] / (1000/ 18)
=> 9 = ([ 270 + x ] * 18) / 1000
=> 9 * 1000 / 18 =270 + x
=> 500 = 270 + x
=> 500 - 270 = x
=> 230 = x
Thus thelength of the second train = 230 metres

• 64. 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?
A.) 3.6 sec
B.) 36 sec
C.) 18 sec
D.) 72 sec

36 sec

• 65. 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:
A.) 36
B.) 45
C.) 48
D.) 49

Relative speed = (60+ 90) km/hr
= ( 150 x 5/18 ) m/sec
= (125/3 ) m/sec
Distance covered = (1.10 + 0.9) km = 2 km = 2000 m.
Required time =( 2000 x 3/125) sec = 48 sec.

• 66. 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?
A.) 40 sec
B.) 42 sec
C.) 45 sec
D.) 48 sec

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

• 67. 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:
A.) 50 m
B.) 72 m
C.) 80 m
D.) 82 m

Let the length of each train be x metres.
Then, distance covered = sum of Length of two trains
= x + x
= 2x metres
Since two trains are moving in the same direction,
Relative speed = faster train speed -slower train speed
=(46 - 36) km/hr
= 10 x (5/18) m/sec
= (25/9) m/sec
Given, Time to passslower train = 36 sec
Therefore, RelativeSpeed = Distance / Time
=> 2x/36 = 25/9
=> 2x = 100
=> x = 50
Hence,length of each train = 50 metres

• 68. A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?
A.) 65 sec
B.) 89 sec
C.) 100 sec
D.) 150 sec

Given, length of the train = 240 m
Time taken by the train to pass the pole = 24 sec
Length of the Platform = 650 m
To find theTime taken by the train to pass the platform:-
Speed of the train = length of the train /Time taken by the train to pass the pole
= (240/ 24 )
= 10 m/sec.
Therefore, Time taken by the train to pass the platform = (length of the train + Length of the Platform) / Speed of the train
= [(240 + 650) / 10] sec
89 sec

• 69. 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?
A.) 120 m
B.) 240 m
C.) 300 m
D.) 250 m

Given,speed of the train = 54 km/hr
---> converting this speed into meter/ sec
=> Speed of the train = (54 x 5 / 18 ) m/sec = 15 m/sec
Given that, thetrain passesa man in 20 seconds.
=> Length of the train = speed of the train *Time to pass theman
= 15 × 20
300 meter
Given that, thetrain passesa platform in 36 seconds.
=> Length of the train + Length of the platform = speed of the train × Time to pass the platform
=> 300 + Length of the platform = 15 × 36
=>Length of the platform = 540 - 300
=>Length of the platform = 240 meter.

• 70. The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
A.) 200 m
B.) 225 m
C.) 245 m
D.) 250 m

Speed = (45x 5/18 ) m/sec = (25/2) m/sec Time = 30 sec.
Let the length of bridge be x metres.
Then, 130 + x /30 = 25/2 => 2(130 + x) = 750 => x = 245 m.

• 71. 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:
A.) 45 km/hr
B.) 50 km/hr
C.) 54 km/hr
D.) 55 km/hr

Given, Length of the train = 125 meter
Time taken by the train to pass the man = 10 sec
Speed of man =5 km/hr
Speed of the train relative to man = (125/10) m/sec
= (25/2)m/sec
=(25/2) x (18/5) km/hr
= 45 km/hr
Let the speed of the train be x km/hr.
Since Man and Train are moving in same direction, speeds must be subtracted
Then, relative speed = Speed of train -Speed of man
=> x - 5 = 45
=> x = 50 km/hr

• 72. A boat is rowed down a river 40 km in 5 hr and up a river 21 km in 7 hr. Find the speed of the boat and the river.
A.) 61/12 kmph
B.) 4.5 kmph
C.) 5 kmph
D.) 5.5 kmph

Speed of the boat downstream = 40/5 = 8 kmph
Speed of the boat upstream = 21/7 = 3 kmph
Speed of the boat = 1/2 ( 8+3) = 11/2 = 5.5 kmph

• 73. A train travels from City X to City Y at a speed of 60 kmph, while on its return journey the train was travelling at speed of 120 kmph. Find the average speed of the train.
A.) 90
B.) 88
C.) 80
D.) 85

Given, Onward journey speed (x) = 60 kmph;
Return journeyspeed (y) = 120 kmph.
Average speed of the train = 2xy / (x + y)
Average speed = (2 x 60 x 120) / (60 + 120 )
= 14400 / 180
Average speed 80 kmph
Average speed of the train = 80 kmph.

• 74. A train travels from City X to City Y at a speed of 32 kmph, while on its return journey the train was travelling at speed of 96 kmph. Find the average speed of the train.
A.) 64
B.) 58
C.) 48
D.) 44

Let x be the speed of the train while going from City X to Y.
Let y be the speed of the train while going from City Y to X.
Average speed of the train is given by = 2xy/(x+y)
Average speed = (2 x 32 x 96) / (32 + 96 ) Average speed = 48

• 75. A train travels from City X to City Y at a speed of 44 kmph, while on its return journey the train was travelling at speed of 77 kmph. Find the average speed of the train.
A.) 56
B.) 58.5
C.) 60
D.) 60.5