# RRB NTPC - Problems on Trains

41.

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

150 m

42.

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

43.

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.) 150 km/hr
B.) 50 km/hr
C.) 75 km/hr
D.) 55 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. Then, relative speed = (x - 5) km/hr.
x - 5 = 45
x = 50 km/hr.

44.

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

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

45.

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

46.

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.) 27 m
B.) 33 m
C.) 27 7/9 m
D.) 23 4/9 m

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.

47.

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

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

48.

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.) 180 m
B.) 200 m
C.) 240 m
D.) 300 m

Given, time taken by train to pass the man = 20 sec
Speed of the train = 54 km/hr
---> Converting into meter/sec
=> Speed of train =54 * (5/18) m/sec = 15 m/sec
W.K.T: Speed of train = Length of train/ Time taken by train to pass the man
=> 15 =Length of train / 20
=>Length of train = 15 * 20
=>Length of train = 300 metre.
Given,A train passes a station platform in 36 seconds.
=>Speed of train = (Length of train + Length of platform) / Time taken by train to pass the platform
=> 15 = (300 +Length of platform) / 36
=> 15 * 36 = (300+Length of platform)
=> 540 =300+Length of platform
=> 540 - 300 =Length of platform
Thus,Length of platform = 240 meter.

49.

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

50.

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

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

51.

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

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

52.

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.

53.

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.

54.

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

350 m

55.

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

56.

Two trains running in opposite directions at 40kmph and 50kmph, cross each other in 30sec. the length of one train is 250m, then find the length of other one?

A.) 440m
B.) 490m
C.) 500m
D.) 510m

L = S×T
L = 90×5/18×30
L = 750m
Length of second train= total length - Length of first train
= 750 - 250 = 500m

57.

Two trains, one from Howrah to Patna and the other from Patna to Howrah, starts 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.) 4:3
C.) 6:7
D.) 9:16

Formula Used:- If two trains start at the same time from points A and B towards each other and after crossing they take a and b hours in reaching B and A respectively, then:
Ratio of their speeds is(A's speed) : (B's speed) = (√b : √a)
Let us name the trains as X and Y. Then,
a = 9 hours
b = 16 hours
Ratio of their speeds = (A's speed) : (B's speed) = √b : √a = √16 : √9 = 4 : 3.

58.

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

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.

59.

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

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 .

60.

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