# 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 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

3.

320m long train is running at 72 Kmph. how much time it will take to cross a platform of 180m long?

A.) 20sec
B.) 25sec
C.) 30sec
D.) 27sec

Answer: Option 'B'

Total Length = platform Length+ Train Length
Total Length= 500m
D = S × T
500 = 72 × time
500 = 72 × 5/18 × time
Time = 25Sec

4.

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

5.

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

6.

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.

7.

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.

8.

A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?

A.) 96 km/hr
B.) 81 km/hr
C.) 51 km/hr
D.) 76 km/hr

Answer: Option 'B'

4.5 km/hr = ( 4.5 x 5/18 ) m/sec = 5/4 m/sec = 1.25 m/sec, and
5.4 km/hr = ( 5.4 x 5/18 ) m/sec = 3/2 m/sec = 1.5 m/sec.
Let the speed of the train be x m/sec.
Then, (x - 1.25) x 8.4 = (x - 1.5) x 8.5
=> 8.4x - 10.5 = 8.5x - 12.75
=> 0.1x = 2.25
=> x = 22.5
Therefore Speed of the train = ( 22.5 x 18/5 ) km/hr = 81 km/hr.

9.

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

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.

10.

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.

11.

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.

12.

A 1200m long train crosses a tree in 120sec, how much time will I take to pass a platform 700m long?

A.) 180sec
B.) 190sec
C.) 170sec
D.) 175sec

Answer: Option 'B'

L = S × T
S= 1200/120
S= 10M/Sec.
Total length(D)= 1900m
T = D/S
T = 1900/10
T = 190Sec

13.

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

14.

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

15.

A 180m long train is running at 72 Kmph. If it crossed the platform in 20sec. then find the platform Length?

A.) 210m
B.) 220m
C.) 240m
D.) 250m

Answer: Option 'B'

Length = Speed*Time
L = 72K.M/H*T
L=72*5/18*20
L= 400M.
Length of Platform= Length-Length of the Train
Length of Platform= 400-180
Length of Platform=220m

16.

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.

17.

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.

18.

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.

19.

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

Answer: Option 'B'

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.

20.

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 .

21.

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

22.

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

Answer: Option 'C'

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

23.

Two trains are running at 60 Kmph and 42 Kmph respectively, in same direction. Fast train completely passes a man sitting in the slower train in 30sec. what is the length of the faster train?

A.) 100m
B.) 125m
C.) 150m
D.) 175m

Answer: Option 'C'

L = S × T
L = 18 × 5/18 × 30
(in same direction Speed = first train - second train)
= 150m

24.

A train crosses a platform of 120m in 15sec, same train crosses another platform of length 180m in 18sec. then find the length of the train?

A.) 175m
B.) 180m
C.) 185m
D.) 170m

Answer: Option 'B'

Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m

25.

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

26.

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

27.

A train 250m long can cross a bridge of length 350m in 20sec, then find the speed of the train?

A.) 30 m/sec
B.) 32 m/sec
C.) 35 m/sec
D.) 36m/sec

Answer: Option 'A'

Length = Speed × Time
Speed= Length/Time
Speed= 600/20
Speed=30 m/sec

28.

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

29.

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

Answer: Option 'B'

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.

30.

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.

31.

A train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is

A.) 560 m
B.) 400 m
C.) 450 m
D.) 600 m

Answer: Option 'B'

Let the length of the first train be x metres.
Then, the length of the second train is (x/2) metres
Relative speed = (48 + 42) kmph
= ( 90 x 5/18 ) m/sec
= 25 m/sec.
Therefore, Time = Length of two trains / Relative speed
=> 12 = [ x + x/2)] / 25
=> 12 = [3x / 2] / 25
=> 3x/2 = 300
=> x = 200
Therefore Length of first train = x = 200 m.
Let the length of platform be y metres.
Speed of the first train = ( 48 x 5/18 ) m/sec
= 40/3 m/sec
Given, the first trainpasses a railway platform in 45 seconds.
Therefore, Time = (Length of the first train + Length of the platform) / speed of the first train
=> (200 + y) x 3/40 = 45
=> 600 + 3y = 1800
=> y = 400 m
So,length of platform = y = 400 m

32.

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.) 50 m
C.) 54 m
D.) 72 m

Answer: Option 'B'

2 kmph = ( 2x 5/18 ) m/sec = 5/9 m/sec 4 kmph = ( 4x 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 ) = 9 and ( x / y - 10 /9 ) = 10 .
Therefore 9y - 5 = x and 10(9y - 10) = 9x => 9y - x = 5 and 90y - 9x = 100.
On solving, we get: x = 50. Therefore Length of the train is 50 m.

33.

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.

34.

A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the second train is:

A.) 48 km/hr
B.) 54 km/hr
C.) 66 km/hr
D.) 82 km/hr

Answer: Option 'D'

Let the speed of the second train be x km/hr.
Relative speed = (x + 50) km/hr = [( x + 50 ) x 5/18 ] m/sec = [ 250 + 5x / 18 ] m/sec.
Distance covered = (108 + 112) = 220 m. 220/ ( 250 + 5x /18 ) = 6 => 250 + 5x = 660 => x = 82 km/hr.

35.

Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?

A.) 10
B.) 12
C.) 15
D.) 20

Answer: Option 'B'

Speed of the first train = ( 120 /10 ) m/sec = 12 m/sec.
Speed of the second train = (120 / 15) m/sec = 8 m/sec.
Relative speed = (12 + 8) = 20 m/sec.
Therefore Required time = [( 120+ 120/ 20)] sec = 12 sec.

36.

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.

37.

A train 110 m long is running with speed of 60 km/hr .In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?

A.) 6 sec
B.) 7 sec
C.) 10 sec
D.) 5 sec

Answer: Option 'A'

Relative speed = Train speed + Man Speed = 60 + 6 = 66 kmph = 18 1/3 m /sec
Distance to be covered = 110 meter
Time taken = Speed / Distance = 110 / (18 1/3) = (110 / 55) x 3 = 2 x 3 = 6 sec

38.

How many seconds will a 500 m 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.) 30
B.) 25
C.) 40
D.) 45

Answer: Option 'A'

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

39.

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.) 76 km/hr
B.) 79.2 km/hr
C.) 79 km/hr
D.) 69.5 km/hr

Answer: Option 'B'

79.2 km/hr

40.

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

41.

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

42.

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

Answer: Option 'C'

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.

43.

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

44.

A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel is:

A.) 540 m
B.) 130 m
C.) 500 m
D.) 260 m

Answer: Option 'C'

Given, Length of the train = 800 m
Speed of the train = 78 km/hr (convert km/hr to m/sec)
= 78 × (5/18) m /sec
= 21.667 m /sec
=> Speed of the train = 21.667 m /sec
Time taken by the train to cross the tunnel = 1 min = 60 sec
To find the length of the tunnel:
Time taken by train to cross tunnel = (Length of tunnel + Length of train) / speed of the train
=> 60 = (Length of tunnel + 800) / 21.667
=> 60 × 21.667 = Length of tunnel + 800
=> 1300 = Length of tunnel + 800
=> 1300 – 800 = Length of tunnel
=> 500 = Length of tunnel
Thus, the Length of tunnel = 500 m

45.

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

A.) 250 m
B.) 245 m
C.) 200 m
D.) 225 m

Answer: Option 'B'

245 m

46.

A train 240 m long passed a pole in 24 seconds .How long will it take to pass a platform 650 m long?

A.) 150 sec
B.) 100 sec
C.) 65 sec
D.) 89 sec

Answer: Option 'D'

89 sec

47.

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

48.

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

49.

How much time does a train 110 metres long running at the speed of 72 km/hr take to cross a bridge 132 metres in length?

A.) 14.3 seconds
B.) 12.1 seconds
C.) 9.8 seconds
D.) 12.42 seconds

Answer: Option 'B'

Given, Length of train = 110 meter
Speed of train =72 km/hr
Length of bridge =132 metre
---> Converting Speed from km/hr into m/sec
=>Speed of train = 72 × (5/18) m/sec
= 4 × 5
20 m/sec
Formula:-Time taken by train to cross the bridge = (Length of the train + Length of the bridge) /Speed of train
= (110 + 132) / 20
= 242/ 20
= 12.1 sec
Thus,Time taken by train to cross the bridge =12.1 seconds

50.

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.