Trains
General Concept:
(1) Time taken by a train x mt long in passing a signal post
or a pole or a standing man = time taken by the train to cover x mt
(2) Time taken by a train x mt long in passing a stationary
object of length y mt = time taken by the train to cover x+y mt
(3) Suppose two trains or two bodies are moving in the same
direction at u kmph and v kmph such that u > v then their
relative speed is u-v kmph
(4)If two trains of length x km and y km are moving in opposite
diredtions at u kmph and vmph,then time taken by the train to
cross each other = (x+y)/(u+v) hr
(5) Suppose two trains or two bdies are moving in opposite direction
at u kmph and v kmph then,their relative speed = (u+v) kmph
(6)If two train start at the same time from 2 points A & B towards
each other and after crossing they take a & b hours in reaching B & A
respectively then A's speed : B's speed = (b^1/2 : a^1/2 )
Problems
(1)Find the time taken by a train 180m long,running at 72kmph in
crossing an electric pole
Solution:
Speed of the train =72*5/18m/s =20 m/s
Distance move din passing the pole = 180m
Requiredtime = 180/20 = 9 seconds
(2)A train 140 m long running at 60kmph.In how much time will it
pass a platform 260m long.
Solution:
Distance travelled =140 + 260 m =400 m,
speed = 60 * 5/18 = 50//3 m
time=400*3 / 50 = 24 Seconds
(3)A man is standing on a railway bridge which is 180 m.He finds
that a train crosses the bridge in 20 seconds but himself in
8 sec. Find the length of the train and its sppeed
Solution:
i)D=180+x
T = 20 seconds
S= 180+x / 20 ------------ 1
ii)D=x
T=8 seconds
D=ST
x=8S ------------- 2
Substitute 2 in 1
S=180 + 8 S / 20
S=15 m/s
Length of the train,x is 8 *15 = 120 m
(4)A train 150m long is running with a speed of 68 mphIn wht
time will it pass a man who is running at a speed of 8kmph in
the same direction in which the train is going
Solution:
Relative Speed = 68-8=60kmph*5/18 = 50/3 m/s
time= 150 * 3 /50 =9sec
5)A train 220m long is running with a speed of 59 k mph /..In
what time will it pass a man who is running at 7 kmph in the
direction opposite to that in which train is going.
Solution:
Relative Speed = 59+7=66kmph*5/18 = 55/3 m/s
time= 220/55 * 3 =12sec
Top
(6)Two trains 137m and 163m in length are running towards each
other on parallel lines,one at the rate of 42kmph & another at
48 mph.In wht time will they be clear of each other from the
moment they meet.
Solution:
Relative speed =42+48 = 90 *5/18 = 25m/s
time taken by the train to pass each other = time taken to cover
(137+163)m at 25 m/s
= 300 /25 s =12 s
(7)A train running at 54 kmph takes 20 sec to pass a platform.
Next it takes 12 sec to pass a man walking at 6kmph in the same
direction in which the train is going.Find length of the train
and length of platform
Solution:
Relative speed w.r.t man = 54-6=48kmph
the length of the train is 48 * 5/18 * 12 =160m
time taken to pass platform =20 sec
Speed of the train = 54 * 5/18 =15m/s
160+x =20 *15
x=140m
length of the platform is 140m
(8)A man sitting in a train which is travelling at 50mph observes
that a goods train travelling in opposite irection takes 9 sec
to pass him .If the goos train is 150m long fin its speed
Solution:
Relative speed =150/9 m/s =60 mph
speed of the train = 60-50 =10kmph
(9)Two trains are moving in the sam e direction at 65kmph and
45kmph. The faster train crosses a man in slower train in18sec.the
length of the faster train is
Solution:
Relative speed =65-45 kmph = 50/9 m/s
Distancce covered in18 s =50/9 * 18 = 100m
the length of the train is 100m
(10)Atrain overtakes two persons who are walking in the same
direction in which the train is going at the rate of 2kmph an
4kmph and passes them completely in 9 sec an 10 sec respectively.
The length of train is
Solution:
2kmph = 5/9 m/s
4 mph =10/9 m/s
Let the length of the trainbe x meters and its speed is y m/s
then x / (y- 5/9) = 9 and x / (y- 10/9) = 10
9y-5 =x and 10(9y-10)=9x
9y-x=5 and 90y-9x=100
on solving we get x=50,lenght of trains
(11) Two stations A & B are 110 km apart on a straight line.
One train starts from A at 7am and travels towards B at 20kmph.
Another train starts from B at 8am an travels toward A at a speed
of 25kmph.At what time will they meet
Solution:
Suppose the train meet x hr after 7am
Distance covered by A in x hr=20x km
20x+25(x-1) = 110
45x=135
x=3
So they meet at 10 am
(12)A traintravelling at 48kmph completely crosses another train
having half its length an travelling inopposite direction at 42kmph
in12 sec.It also passes a railway platform in 45sec.the length of
platform is
Solution:
Let the length of the first train be x mt
then,the length of second train is x/2 mt
relative speed = 48+42 kmph =90 * 5/18 m/s = 25m/s
(x+ x/2)/25 =12
x=200
Length of the train is 200m
Let the length of the platform be y mt
speed f the first train = 48*5/18 m/s = 40/3 m/s
200+y * 3/40 = 45
y=400m
Top
(13)The length of a running trsain in 30% more than the length of
another train B runnng in the opposite direction.To find out the
speed of trtain B,which of the following information given in the
statements P & Q is sufficient
P : The speed of train A is 80 kmph
Q : They too 90 sec to cross each other
(a) Either P & Q is sufficient
(b)Both P & Q are not sufficient
(c)only Q is sufficient
(d)Both P & Q are neeed
Ans: B
Solution:
Let the length of th e train A be x mt
Length of the train B = 130/100 x mt =13x/10 mt
Let the speed of B be y mph,speed of the train A=80mph
relative speed= y+80 * 5/18 m/s
time taken by the trains t cross each other is gven by
90 = (x + 13x/10)/ (5y+400 / 18)
to find y,clearly xis also needed
so,both P & Q are not sufficient
(14)The speed of a train A,100m long is 40% more than then the speed
of another train B,180m long running in opposite direction.To fin out
the speed of B,which of the information given in statements P & Q is
sufficient
P :The two trains crossed each other in 6 seconds
Q : The difference between the spee of the trains is 26kmph
(a)Only P is sufficient
(b)Only Q is sufficient
(c)Both P & Q are needed
(d)Both P & Q are not sufficient
Ans : A
Solution:
Let speed of B be x kmph
then,speed of A =140x/100 kmph =7x/5 mph
relative speed = x + 7x/5 =2x/3 m/s
time taken to cross each other = (100+180)*3/2x s =420/x s
now,420/x = 6
x=70 mph
thus,only P is sufficient
(15)The train running at certain speed crosses astationary enginein
20 seconds.to find out the sped of the train,which of the following
information is necessary
(a)Only the length of the train
(b)only the length of the engine
(c)Either the length of the train or length of engine
(d)Both the length of the train or length of engine
Ans : D
Solution:
Since the sum of lengths of the tran and the engine is needed,
so both the length must be known
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