##
__Problems on Trains __

__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 train is taken into
consideration.

**1.**The distance travelled by a 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 a 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 train and the length of the 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.**Time taken by a train to cross an object of negligible length =

Length of the train
Speed of the train

**4.**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 same direction, then their relative speed = (x-y)

**e.g**If two trains with speeds 30 kmph and 40 kmph are running in same direction, then their relative speed = 40-30= 10 kmph

**6.**If two trains with speeds x kmph and y kmph are moving in opposite direction, then their relative speed = (x+y) kmph

**e.g**if two trains with speeds 30 kmph and 40 kmph are running in opposite direction, then their relative speed = 30 +40 = 70 kmph

**Problems on Trains – Solved Problems**

**1.**

**A train is running at 48 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 time given in seconds

We
need to convert 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 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 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 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 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 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 opposite direction, the relative velocity= (x+6) kmph

As distance in meters and time is in seconds.
Converting (x+6) kmph into m/s

Distance = Speed x Time => 360
= (x+6)x

5
18

x18 => X=
72-6= 66 kmph**5. The time taken by a train running at the speed of 45 kmph of length 270m to cross a stationary train of length 280 m , is**

**a)**

**24 seconds b)30 seconds c)36 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= 450 m

Time taken = Total distance to be travelled/
Speed of the train =

450
45

x
18
5

= 36 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 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 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 ong 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 opposite direction,
relative speed= sum of their speeds = 36+44= 80 kmph

But
speed 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 platform=240+720= 960m.

Length of the train + Length of the platform=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 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 460m long train moving with an average speed of 54 kmph crosses a platform in 12 seconds. A man crosses the same platform in 40 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
length of the train is 460m

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

=
(460+x) meters

Time
taken to cross platform= 12s

Speed
of the train = 54 kmph = 54 x

5
18

= 15 m/s
Speed=

Distance
Time

=> 45=> =
(460+x)
12

=>x=280
Length
of the platform= 280m

Time
taken by man to cross the platform= 40 seconds

Therefore
Speed of man =

Lenght of platform
Time taken 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 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
length of the 2

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

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

Speed
in both cases is same

=>

Distance to cross stationary train
Time taken to cross the pole

=
Distance to cross the pole
Time talke 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 =

Decrease in Distance
Original Distance

x 60 minutes
=

9
45

x 60 = 12 minutes.**14. The distance between 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 Speed

=>
540
90

= 6 hours
The
train which starts from 2

^{nd}station must travel (6x40) = 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

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), 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=

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.
Time they meet each other = 8 a.m. + 4
hours =12 p.m