Problems on Trains
The questions based
on trains are solved in the same manner as the problems of time and distance
are solved but here the length of the train is taken into consideration.
1.
The distance travelled by train to
pass a pole or a standing man or tree or any other object of negligible length
is equal to the length of the train
e.g. The distance covered by a 150 m long
train in passing a tree = 150m
2.
The distance travelled by train to
pass a platform or another train or bridge or railway station or any other object having some considerable
length is equal to the sum of the lengths of the train and the length of that
particular object ( another train or platform or bridge)
e.g. The distance travelled by a 250m long train to
cross a bridge of length 150m = Sum of the lengths of train and bridge = (250 +
150) = 400 m
3.
The time taken by a train to cross an
object of negligible length = Length of the train/ Speed of the train
4.
The time taken by a train to cross an
object of considerable length =
( Length of the train+
Length of another train )/ Speed of the train
5.
If two trains with speeds x kmph and y
kmph ( where x>) are moving in the same direction, then their relative speed
= (x-y)
e.g If two trains with speeds 30 kmph and 40 kmph are
running in the same direction,
then their relative speed = (40-30)= 10 kmph
6.
If two trains with speeds x kmph and y
kmph are moving in the opposite direction, then their relative speed = (x+y)
kmph
e.g if two
trains with speeds 30 kmph and 40 kmph are running in the opposite direction,
then their relative speed = (30 +40))= 70 kmph
Problems
on Trains – Solved Problems
1. A train is running at 54 kmph. If it crosses a pole in 35
seconds, then its length is
a)
450m b)500 m c)525m d)560m
Answer:C
Explanation: The
speed of train = 54 kmph but the time is in seconds
Converting the
speed into m/s. => 54 x 5/18 =15 m/s
Time taken = 35 seconds.
Therefore, length
of the train= Distance travelled by the train to cross a pole
= (Speed x Time0 = (15 x 35) = 525 m
2. A
560m long train crosses a standing man in 80 seconds. What is the speed of the
train?
a)4
m/s b)5 m/s c)6
m/s d)7 m/s
Answer:
D
Explanation: Distance
covered by the train is equal to the length of the train ( since it is crossing
a standing man whose length is negligible)
Distance covered = 560
m
Time taken = 80 s
Therefore, Speed of
the train= Distance covered/ Time taken= 560/80 = 7 m/s
3. The
speed of two trains are in the ratio 7:9. If the second train runs 405 km in 5
hours, then the speed of the first train is
a)
63 kmph b)72 kmph c)81 kmph d)90
kmph
Answer: A
Explanation:
Speed
of the second train = Distance/ Time = 405/5= 81 kmph
Let the speeds of trains be 7x and 9x
kmph respectively.
Speed of 2nd train
=9x= 81 kmph => x = 9 kmph
Speed of the first train= 7x = 7 x 9 kmph
= 63 kmph.
4. A
train 360 m long passes a man walking along the line in the opposite direction
at the rate of 6 kmph in 18 seconds. Find the speed of the train?
a) 60 kmph b)66 kmph c)72
kmph d)75
kmph
Answer:
B
Explanation:
Let the speed of the train be x kmph
Speed of the man= 6 kmph
Distance travelled
= Length of the train = 360m
As both are moving in
the opposite direction, the relative speed=
(x+6) kmph
As distance is in meters and time is in
seconds. Converting (x+6) kmph into m/s
Distance = Speed x Time
ð 360
= (x+6) x 5/18 x 18
ð X=
72-6= 66 kmph
5. The
time taken by a 270 m long train which is running at the speed of 45 kmph to cross
a stationary train of length 280 m , is
a)
24 seconds b)30 seconds c)44 seconds d)48
seconds
Answer
:C
Explanation:
Speed of the train = 45 kmph = 45 x 5/18 m/s
Total distance=
Length of the moving train + Length of the stationary train
=270+280= 550 m
Time taken = Total distance to be travelled/
Speed of the train
= 550/45 x 18/5 = 44 seconds
6. Two
trains of lengths 60m and 80m are moving in opposite directions at the speeds
of 9 m/s and 5 m/s . The time taken to cross each other is
a)10
seconds b)8
second c)6 seconds d)15 seconds
Answer:A
Explanation:
Distance to be travelled= Sum of the
lenths of the two trains= (60m +80m) = 140m
Two
trains are moving in the opposite
direction, their relative velocity = (9+5) = 14 m/s
Time taken to cross each other = Distance /
Speed= 140/14 = 10 seconds.
7 Two
trains 105 m and 135 m long are running towards each other on parallel lines at
a speed of 36 kmph and 44 kmph respectively. To cross each other after they
meet, it will take
a)
8 seconds b)9 seconds c)10.8
seconds d)15 seconds
Answer:C
Explanation:
Distance covered= Sum of the lengths
of two trains= 105+135= 240 m.
They are moving in the opposite direction,
relative speed= sum of their speeds = 36+44= 80 kmph
But speed is in kmph and distance is
in meters. We convert the speed into m/s.
= 80 kmph x 5/18
Time taken = Distance/ Speed = 240/
80 x 18/5 =10.8 seconds
8.A 240m
long train crosses a bridge of thrice its length in 4 minutes. Find the speed
of the train?
a)
3 seconds b)4
seconds c)5
seconds d)6
seconds
Answer:
B
Explanation: Length
of the train is 240m
So length of the bridge
= 3 x 240 = 720 m
Time taken to cross
bridge= 4 minutes = 240 seconds
Total distance
travelled= Length of the train + Length of the bridge
= (240+720)= 960m.
Speed of the train =Distance Covered/Time
Taken
= 960/240 = 4
seconds
9. A
train crossed a platform in 48 seconds. The train is running at a speed of 10
m/s What is the length of the platform if the length of the train is 320m?
a)160m b)220m c)250m d)280m
Answer:A
Explanation:
Let
the length of the platform be x meters
Length of the train = 320m
Time taken to cross
platform= 48 seconds
Distance covered by
the train to cross the platform= Length of the train + length of the platform
=(320+x) meters.
Time=
Distance/Speed => 48 seconds = (320+x)/10
=>x = (480-320)=160 meters
10. A 440m long train moving with an average speed of 54 kmph
crosses a platform in 48 seconds. A man crosses the same platform in 70
seconds. What is the speed of the man?
a)
5 m/s b)4 m/s c)7
m/s d)8m/s
Answer:B
Explanation:
Let the length of the platform be x meters
Length of the train is 440m
Distance to be
covered by train to cross platform= Sum of the lengths of train and the platform
=
(440+x) meters
Time taken to cross
the platform= 48 seconds
Speed of the train
= 54 kmph = 54 x 5/18 = 15 m/s
Speed= Distance/Time => 15= = (440+X)/48 =>x=280
Length of the
platform= 280m
Time taken by man
to cross the platform= 70 seconds
Therefore , the speed
of man =Length of the platform/ Time taken by the man to cross the platform
= 280/70= 4 m/s
11. A
train travelling with a speed of 80 kmph catches another train travelling in
the same direction and then leaves it 150 meters behind in 12 seconds. What is
the speed of the second train?
a)25 kmph b)30 kmph c)35
kmph d)40
kmph
Answer:C
Explanation:
Speed of first train= 80 kmph
Let the speed of 2nd train be x.
Both are moving in
same direction, so their relative speed= 80+x
Speed =
Distance/Time => (80-x)=150/12 x 18/5
=>
(80-x)=45=>x=35
Speed of the 2nd train= 35 kmph.
12.
Train A crosses a stationary train in 50 seconds and a pole in 30 seconds with
the same speed, The length of train A is 300m. Find the length of another
train?
a)200
meters b)250 meters c)350 meters d)400
meters
Answer:A
Explanation:
The length of the first train is 300m
Let the length of
the 2nd train be x meters.
Distance to be
travelled to cross the pole = Length of the train A = 300 m
Distance to be travelled
to cross the stationary train = (Length of the train A + Length of the
stationary train) = (300+x)
Speed in both cases
is the same
=> Distance to
be travelled to cross the stationary train / Time taken to cross the pole= Distance
to be travelled to cross the pole /Time taken to cross the pole.
=> (300+x)/50 =
300/30
=> x=200 meters
Length of the
stationary train= 200 meters
13.
The average speed of a train including stoppages was 36 kmph and excluding
stoppages was 45 kmph . How many minutes per hour did the train stop?
a)6
minutes b)8
minutes c)10
minutes d)12
minutes
Answer:D
Explanation:
The train travels
36 km per hour including stoppages and 45 km per hour excluding stoppages.
Because of the
stops, the train runs (45 -36) = 9 km less per hour
Number of minutes did the train stop per hour=
Decrease in the distance/ Original distance x 60 minutes
= 9/45 x 60 = 12 minutes.
14.
The distance between the two stations is 540 km. A train starts from the first
station towards the 2nd station at 50 kmph and at the same time
another train starts from the 2nd station towards the first station
at 40 kmph. Where will they meet from the 2nd station?
a)
300 km b)240 km c)150 km d)275 km
Answer:
B
Explanation:
Two trains are moving in opposite
direction=> Their relative speed= Sum of their speeds = 40 +50 = 90 kmph
Time to travel the
distance of 540 km => Distance/ Relative velocity => 540/90 = 6 hours
The train which
starts from 2nd station must travel ( 6 x 40 ) = 240 km to meet the
another train coming in opposite direction
15.
The distance between 2 stations A and B is 330 km. A train starts from A at a
speed of 50 kmph at 7 a.m towards B. Another train starts from B towards A at 8
p.m at a speed of 20 kmph. At what time will they meet each other?
a)10 a.m b)12 P.M c)1.30 pm d)2.15
pm
Answer
: B
Explanation:
Distance = 330 km
A Train starts from A at a speed of 50 kmph
at 7 a.m.
Another Train starts from B at a speed of 20 kmph at 8.a.m
From 7 a.m. to 8 a.m.(
in hour), the distance travelled by train starts from A = 50 km
Remaining distance= 330-50= 280 km
Relative speed of two trains = 50 + 20 = 70
kmph
Time taken to travel 280 km= Distance/
Speed = 280/70= 4 hours
After 4 hours from when the 2nd
train starts, they will meet each other.
They meet each other at= 8 a.m. + 4
hours =12 p.m