RRB NTPC - Problems on Trains

1.

A 400m long train is running at 72 Kmph. how much time it will take to cross an electric pole? 

   A.) 15sec
   B.) 20sec
   C.) 19sec
   D.) 21sec

Answer: Option 'B'

Formula: Distance = Speed × Time
If we convert Kmph in to Mpsec multiply by 5/18,
400 = 72 KmpH × time
400 = 72×5/18 × time
Time = 20Sec

2.

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

3.

A train 280 m long, running with a speed of 63 km/hr will pass a tree in:

   A.) 15 seconds
   B.) 20 seconds
   C.) 16 seconds
   D.) 18 seconds

Answer: Option 'C'

Given
Length of the train = 280 m
Speed of the train = 63 km / hr
---> To convertkm/hr to m/sec multiply speed with (5 / 18)
= 63 x (5 / 18) m/sec
= 17.5 m/sec
ThereforeSpeed of the train =17.5m/sec
Now,Time taken by the train tocross an electric pole =Length of the train/Speed of the train
= 280/17.5
16 sec
The time taken is16 sec.

4.

A train crosses a tree in 120sec, while it crosses a 700m long platform in 190sec. the length of the Train is: 

   A.) 1500m
   B.) 1400m
   C.) 1300m
   D.) 1200m

Answer: Option 'D'

In 190Sec Cross a 700m Platform I.e., 
Length of Train + Length of Platform. 
190 Sec- 120Sec = 700m 
70Sec= 700m 
Speed= 10 M/Sec 
In 120 Sec The length wil be 1200m. 

5.

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

Answer: Option 'B'

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

6.

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

Answer: Option 'C'

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.

7.

The two trains of lengths 400m, 600m respectively, running at same directions. The faster train can Cross the slower train in 180sec, the speed of the slower train is 48km. then find the speed of the Faster train? 

   A.) 58 Kmph
   B.) 68 Kmph
   C.) 78 kmph
   D.) 55 Kmph

Answer: Option 'B'

Length of the two trains = 600m + 400m 
Speed of the first train = X 
Speed of the second train= 48 Kmph 
1000/X - 48 = 180 
1000/x - 48 * 5/18 = 180 
50 = 9X - 120 
X = 68 Kmph 

8.

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

9.

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

10.

A 600 m long train crosses a pole in 9 sec, What is the speed of the train Km/hr ?  

   A.) 240
   B.) 280
   C.) 260
   D.) 220

Answer: Option 'A'

Speed of the train = Length / Time taken
=> 600 / 9 m /sec
= 200 / 3 m/sec
We need in kmph,
Speed = (20/3) x (18/5)
240 kmph

11.

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

Answer: Option 'B'

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.

12.

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

Answer: Option 'B'

36 sec

13.

Two trains 300m and 400m long run at the speeds of 40 kmph and 50kmph respectively in opposite Directions on parallel tracks. The time taken to cross each other? 

   A.) 20sec
   B.) 25secs
   C.) 26sec
   D.) 28sec

Answer: Option 'D'

Length of two Trains = 300m + 400m = 700m 
Total Speed= 40 Kmph + 50 Kmph (Opposite Direction)
= 90 Kmph 
Time = Distance/Speed 
Time = 700/ 90 
Time = 28Sec

14.

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.

15.

A 600m long train is running at 90 Kmph. how much time it will take to cross an electric pole? 

   A.) 16sec
   B.) 20sec
   C.) 24sec
   D.) 22sec

Answer: Option 'C'

Formula: D = S × T 
600 = 90 Kmph × T 
600 = 90 × 5/18 × T 
Time = 24Sec

16.

Two, 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: 

   A.) 2 : 3
   B.) 6 : 7
   C.) 4 : 3
   D.) 9 : 16

Answer: Option 'C'

Let us name the trains as A and B. Then,
(A's speed) : (B's speed) = √b : √a = √16 : √9 = 4 : 3.

17.

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

18.

A 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: 

   A.) 45 m
   B.) 55 m
   C.) 50 m
   D.) 65 m

Answer: Option 'C'

2 kmph = (2 x 5/18) m/sec = 5/9 m/sec.
4 kmph = (4 x 5/18 m/sec = 10/9 m/sec.
Let the length of the train be x metres and its speed by y m/sec.
Then, ( x/(y - 5) = 9 and ( x/(y - 10) = 10.
Therefore 9y - 5 = x and 10(9y - 10) = 9x
=> 9y - x = 5 and 90y - 9x = 100.
On solving, we get: x = 50.

19.

 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 

20.

Two 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?

   A.) 23 m
   B.) 23 (2/9 ) m
   C.) 27 (7/9 ) m
   D.) 29 m

Answer: Option 'C'

Relative speed = (40 - 20) km/hr = ( 20 x 5/18 ) m/sec = (50/9) m/sec
Therefore, Length of faster train = ( 50/9 x 5) m = 250/9 m = 27 (7/9 ) m.


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