RRB NTPC - Problems on Trains

1.

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.

2.

Two 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:

   A.) 3 : 2
   B.) 1 : 3
   C.) 3 : 7
   D.) 3 : 4

Answer: Option 'A'

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)/(x + y) = 23
27x + 17y = 23x + 23y
4x = 6y
x/y = 3/2 .

3.

 A 240m long train is running at 90kmph. If it crossed the platform in 30sec, then find the length of the platform?

   A.) 490m
   B.) 500m
   C.) 510m
   D.) 550m

Answer: Option 'C'

L = S × T 
L=90×5/18×30 
L=750m 
Length of Platform= Length-Length of the Train = 750 – 240 = 510m 

4.

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

5.

A train is running at 72 Kmph. It was crossed an electronic pole in 20sec. find the length of the train? 

   A.) 300m
   B.) 400m
   C.) 250m
   D.) 405m

Answer: Option 'B'

L = S × T 
L = 72 Kmph × 20Sec 
L = 72 × 5/18 × 20 
L = 400m 

6.

A 180m long train is running at 54 Kmph. how much time it will take to cross a platform of 120m long? 

   A.) 20sec
   B.) 22sec
   C.) 19sec
   D.) 18sec

Answer: Option 'A'

Formula: D = S × T 
180 = 54 Kmph × Time 
180= 54×5/18 × Time 
Time = 20 Sec 

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: 

   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

8.

A train 400m long can cross an electric pole in 20sec, then find the speed of the train? 

   A.) 65 Kmph
   B.) 70 Kmph
   C.) 72 Kmph
   D.) 75 Kmph

Answer: Option 'C'

Length = Speed × time 
Speed = L/T 
S = 400/20 
S = 20 M/Sec 
Speed= 20×18/5 (To convert M/Sec in to Kmph multiply by 18/5) 
Speed = 72 Kmph 

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.

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

11.

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
   D.) Data inadequate

Answer: Option 'B'

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.

12.

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

Answer: Option 'A'

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

13.

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

Answer: Option 'A'

12 sec

14.

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

Answer: Option 'D'

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.

15.

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

16.

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

Answer: Option 'B'

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.

17.

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:  

   A.) 10
   B.) 18
   C.) 72
   D.) 36

Answer: Option 'D'

Given, Length of each train = 120 metres.
Let the speed of each train be x m/sec.
Then, relative speed of the two trains = x + x = 2x m/sec.
So, Speed = Distance / Time
=> Relative Speed of two trains = (Sum of length of two trains) / Time taken to cross each other.
=> 2x = (120 + 120 ) / 12
=> 2x = 20
=> x = 10.
Therefore,Speed of each train = 10 m/sec = ( 10 x 18/5 ) km/hr = 36 km/hr.

18.

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

Answer: Option 'A'

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 44 x 77) / (44 + 77 )
Average speed = 56

19.

A 300 m long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds .What is the length of the platform?

   A.) 350 m
   B.) 650 m
   C.) 320 m
   D.) 500 m

Answer: Option 'A'

350 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.) 150 m
   B.) 160 m
   C.) 240 m
   D.) 250 m

Answer: Option 'A'

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


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