### APTITUDE – Problems on 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

**(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

(**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

the speed of the train is 10kmph crossing a man in 10sec , what is the length of the train??

speed of train =10kmph=10*5/18

time=10s

distance=speed*time

=10*5/18*10=27.77km

27.77m

250/9

25.5m

if train A left at 1 am from a station at a x mph , Train B left

from same staion at 2 am then

at what will be speed of train B to meet train A at newyork station at 5.30 pm

options were in fration of x like

bakwaaas question ………….dimaag ka shotttttt

15.75*x

Two trains start from stations A and B spaced 50km apart at the same time and speed.As the trains start,a bird flies from one train towards the other and on reaching the second train,it flies back to the first train. This is repeated till the trains collide.If the speed of the trains is 25km/hr come that of the bird is 100km/hr.How much did the bird travel till the collision?

answer to the said question is 100 km .

two trains are moving towards each other at 25km/hr then relative speed wud be 50km/hr.time taken wud be 1 hr to cover 50 km and the bird also flies till 1 hour .so the distance travel wud be….100 km.

ans:100kms…

d=s*t;

as two trains move in opposite direction so sum up the speed of two trains…this is called as relative speed…

time taken for two trains to collide=50/50=1

speed of the bird is 100 km/ph….

d=100*1=100kms

which pump is used for molten metal flow

100

two trains start at same time from delhi and pune and proceeds towards eachother at the rate of 80k/h and 90k/m respectively.when they meet it is found that one train has travelled 200km more than the other.find the distance b/n delhi and pune

let the time after they meet is=t

distance traveled by train from delhi in t time = 80* t

distance traveled by train from pune in t time = 90*t

so

90t-80t=200

t=20

A=distance traveled by train from delhi in 20 hours=80*20

B=distance traveled by train from pune in 20 hours =90*20

total distance =A+B

2 TRAINS ME LENGTH 200 AND 100M IF MOVING IN SAME DIRECTION TAKES 30 SEC TO CROSS. IF MOVING IN OPPOSITE DIRECTIONS TAKE 20 SEC. WHATARE THE PREFER OF THE TRAINS?

100km

@ sandesh gavandi

speed of second train =y

speed of first train =x

time diffrence between trains 1 hour

and time to reach for second train is 3.5 hours

so now distance are same for both so

x= vt

y* 3.5= X* 4.5

y=4.5x/3.5

v=1.28x

.

let speed of 1st train be x

let speed of 2nd train be y

time difference is 1 hr.

distance travelled is same for both the trains

d=s*t

x*33\2=d=y*31\2

x*33*2/2*31=y

x*33/31=y

y=1.065x