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* *__Problems on Trains__ – Important Points to Remember :

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
150 m long train in a 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 54kmph. 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 given in seconds
We need to convert the speed into m/s. => 54 x
5/18 =15 m/s
Time taken = 35 seconds.
Therefore, the length of the train= Distance travelled by
train to cross a pole
=
(Speed x Time) = (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 the length of
the train ( since it is crossing a standing man whose length is negligible)
Distance covered = 560m
Time taken = 80 s
Therefore, Speed of the train= Distance covered/ Time taken=
560/80 = 7 m/s

*3.** **The speeds 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 2^{nd} 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
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 in meters and time is in seconds.
Converting (x+6) kmph into m/s
Distance = Speed x Time Ã° 360
= (x+6) x 5/18 x 18 Ã° x = (72-6)= 66 kmph

* **5**. **The
time taken by a 270m long train 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 speeds of 9 m/s and 5 m/s . The time taken to
cross each other is*
*a)10
seconds
b)8
seconds
c)6 seconds
d)15 seconds*
Answer:A
Explanation:
Distance to be travelled= Sum of
the lengths of the two trains
= (60m +80m) = 140m
Two trains are moving in 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 105m and 135m long are running towards each other
on parallel lines at the speeds 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 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 platform = (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 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)6
m/s
c)7
m/s
d)8m/s*
Answer: B
Explanation:
Let
the length of the platform be x meters
Given that the length of the train is 460m
Distance covered by train to cross platform= Sum of the
lengths of train and 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 m
Length of the platform= 280 m
Time taken by man to cross the platform= 40 seconds
Therefore Speed of man =Length of the platform/ Time taken
by man to cross platform
=
280/40= 7 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 2^{nd} 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 2^{nd} 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 the 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:
Length of the first train is 300m
Let the length of the 2^{nd} train be x meters.
Distance to be travelled to cross a pole = Length of the
train A = 300 m
Distance to be travelled to cross stationary train = (Length
of the train A + Length of the stationary train) = (300+x)
Speed in both cases is the same
=> Distance to cross stationary train/ Time taken to cross
the pole = Distance 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 these stops, the train runs (45 -36) = 9 km less
per hour
Number of minutes did the train stop per hour
= Decrease 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 2*^{nd} station at 50 kmph and
at the same time another train starts from the 2^{nd} station
towards the first station at 40 kmph. Where will they meet from the 2^{nd} 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 2^{nd} station must
travel ( 6 x 40 ) = 240 km to meet another train coming in the 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 an 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 2^{nd} train starts, they will meet each other.
They meet each
other at= (8 a.m. + 4 hours) =12 p.m.

__Problems on Trains__ – Important Points to Remember :
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
150 m long train in a 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 54kmph. 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 given in seconds

We need to convert the speed into m/s. => 54 x
5/18 =15 m/s

Time taken = 35 seconds.

Therefore, the length of the train= Distance travelled by
train to cross a pole

=
(Speed x Time) = (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 the length of
the train ( since it is crossing a standing man whose length is negligible)

Distance covered = 560m

Time taken = 80 s

Therefore, Speed of the train= Distance covered/ Time taken=
560/80 = 7 m/s

*3.*

*The speeds 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 2

^{nd}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
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 in meters and time is in seconds.
Converting (x+6) kmph into m/s

Distance = Speed x Time Ã° 360
= (x+6) x 5/18 x 18 Ã° x = (72-6)= 66 kmph

*5*

*.*

*The time taken by a 270m long train 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 speeds of 9 m/s and 5 m/s . The time taken to cross each other is*

*a)10 seconds b)8 seconds c)6 seconds d)15 seconds*

Answer:A

Explanation:

Distance to be travelled= Sum of
the lengths of the two trains

= (60m +80m) = 140m

Two trains are moving in 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 105m and 135m long are running towards each other on parallel lines at the speeds 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 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 platform = (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 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)6 m/s c)7 m/s d)8m/s*

Answer: B

Explanation:

Let
the length of the platform be x meters

Given that the length of the train is 460m

Distance covered by train to cross platform= Sum of the
lengths of train and 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 m

Length of the platform= 280 m

Time taken by man to cross the platform= 40 seconds

Therefore Speed of man =Length of the platform/ Time taken
by man to cross platform

=
280/40= 7 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 2

^{nd}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 2

^{nd}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 the 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:

Length of the first train is 300m

Let the length of the 2

^{nd}train be x meters.
Distance to be travelled to cross a pole = Length of the
train A = 300 m

Distance to be travelled to cross stationary train = (Length
of the train A + Length of the stationary train) = (300+x)

Speed in both cases is the same

=> Distance to cross stationary train/ Time taken to cross
the pole = Distance 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 these stops, the train runs (45 -36) = 9 km less
per hour

Number of minutes did the train stop per hour

= Decrease 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 2*^{nd}station at 50 kmph and at the same time another train starts from the 2^{nd}station towards the first station at 40 kmph. Where will they meet from the 2^{nd}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 2

^{nd}station must travel ( 6 x 40 ) = 240 km to meet another train coming in the 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 an 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 2

^{nd}train starts, they will meet each other.
They meet each
other at= (8 a.m. + 4 hours) =12 p.m.