RRB NTPC - 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?

   A.) 120 m
   B.) 140 m
   C.) 150 m
   D.) 135 m

Answer: Option 'C'

Speed = ( 60 x 5/18) m/sec = 50/3 m/sec Length of the train = Speed x Time = (50/3) x 9 = 150 m

2.

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

Answer: Option 'D'

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

3.

A man can row 30 km upstream and 44 km downstream in 10 hrs. It is also known that he can row 40 km upstream and 55 km downstream in 13 hrs.Find the speed of the man in still water

   A.) 8 km/hr
   B.) 6 km/hr
   C.) 12 km/hr
   D.) 4 km/hr

Answer: Option 'A'

Let the speed of the man in still water be x kmph and speed of the stream be y kmph
Downstream speed = x+y kmph and
Upstream Speed = x-y kmph
=>30 / (x-y) + 44 / (x+y) = 10 and
40 / (x-y) + 55 / (x+y) = 13
Let 1/ (x+y) = u and 1/ (x-y) = v
----> 30 u + 44 v = 10 ---> multiply this eqn by 4
----> 40 u + 55 v = 13 ---> multiply this eqn by3
Solving these two linear equation we get u = 1/5 and v = 1/11
----> x - y = 5 and x+y = 11
Solving these two linear equation we get
-----> x = 8 and y = 3
So the speed of the man in still water = x = 8 km/ph

4.

A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 seconds .What is the length of the goods train?

   A.) 270 m
   B.) 250 m
   C.) 130 m
   D.) 230 m

Answer: Option 'A'

270 m

5.

A train 130 m long passes a bridge in 21 sec moving with a speed of the 90 km/hr. Find the length of the bridge.

   A.) 415
   B.) 395
   C.) 405
   D.) 385

Answer: Option 'B'

Speed of the train = (Train length + Bridge Length ) / time taken to cross the bridge
=> 90 * (5/18)= (130 + Bridge Length) / 21
=> 25 =(130 + Bridge Length) / 21
=> 130 +Bridge Length = 21 x 25
=>130 +Bridge Length =525
=> Bridge Length = 525 - 130
=>Bridge Length = 395 m

6.

A train is running at 108 Kmph. It was crossed an electronic pole in 28sec. find the length of the train? 

   A.) 480m
   B.) 840m
   C.) 640m
   D.) 740m

Answer: Option 'B'

L = S × T 
L = 108 Kmph × 28Sec 
L =108 × 5/18 × 28 
L= 840m

7.

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

Answer: Option 'B'

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 .

8.

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

Answer: Option 'C'

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.

9.

A train crosses a platform of 150m in 15sec, same train crosses another platform of length 250m in 20sec. then find the length of the train? 

   A.) 150m
   B.) 165m
   C.) 155m
   D.) 160m

Answer: Option 'A'

Length of the train be ‘X’ 
X + 150/15 = X + 250/20 
4X + 600 = 3X + 750 
X = 150m 

10.

Two 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?

   A.) 9 a.m.
   B.) 10 a.m.
   C.) 10.30 a.m.
   D.) 11 a.m.

Answer: Option 'B'

Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110 => 45x = 135 => x = 3.
So, they meet at 10 a.m.

11.

The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is: 

   A.) 150 m
   B.) 160 m
   C.) 240 m
   D.) 245 m

Answer: Option 'D'

Speed = 45 x 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.

12.

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.) 48 seconds
   B.) 42 seconds
   C.) 40 seconds
   D.) 45 seconds

Answer: Option 'C'

Given, Length of train =360 m
Length of bridge =140 m
Speed of train = 45 km/hr ---> Converting into meter/ second
= 45 × (5/18) m / sec
= 12.5 m/sec
=>Speed of train =12.5 m/sec
Required Time =(Length of train + Length of bridge) /Speed of train
= (360 + 140) / 12.5
= 500 / 12.5
= 40 sec
=>Required Time =40 sec

13.

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

Answer: Option 'B'

7 1/2 sec

14.

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.) 150 m
   B.) 160 m
   C.) 240 m
   D.) 250 m

Answer: Option 'C'

Speed = 54 x 5/18 m/sec = 15 m/sec. 
Length of the train = (15 x 20)m = 300 m.
Let the length of the platform be x metres.
Then, (x + 300)/36 = 15
x + 300 = 540
x = 240 m.

15.

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

Answer: Option 'A'

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

16.

A train speeds past pole in 15 seconds and a platform 100 m long in 25 seconds ,its length is:

   A.) 100 m
   B.) 200 m
   C.) 150 m
   D.) 50 m

Answer: Option 'C'

150 m

17.

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

Answer: Option 'A'

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

18.

Two trains 145 m and 155 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time taken by them to completely cross each other in seconds is

   A.) 10.8
   B.) 9.5
   C.) 10.75
   D.) 11

Answer: Option 'A'

Given, Length of 1st train = 145 m
Length of 2nd train = 155 m
Total length of two trains = 145 + 155 = 300 m
Speed of1st train = 60 kmph
Speed of 2nd train = 40 kmph
Since the two trains are moving in opposite direction, speed can be added.
=> Relative speed = Speed of1st train +Speed of 2nd train
60 + 40 = 100 kmph
--> Converting into m/sec
= 100 x (5/18) m/sec
= 250 / 9 m/sec
=>Relative speed =250 / 9 m/sec
Time taken by the trains to completely cross each other
 = Total length of two trains /Relative speed
= 300/ (250 /9)
= (300 × 9) / 250
=2700 / 250
= 10.8 sec
Thus,Time taken by the trains to completely cross each other = 10.8 sec

19.

Two 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? 

   A.) 10 a.m.
   B.) 11 a.m.
   C.) 8 a.m.
   D.) 9 a.m.

Answer: Option 'A'

Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
=> 45x = 135
=> x = 3.
So, they meet at 10 a.m.

20.

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

   A.) 120 m
   B.) 324 m
   C.) 150 m
   D.) 200 m

Answer: Option 'C'

150 m


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