# 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

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

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

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

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

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

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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 .