Aptitude - Problems on Trains - Discussion

23-17/27-23=6:4 or 3:2 (LINK-UP METHOD)

Thanku Anjan :).

If Two trains of length a metres and b metres are moving in opposite directions at u m/s and v m/s, then the time taken by the trains to cross each other=(a+b)/(u+v)sec.

a=27x, b=27y, u=x, v=y.

Lets speed of 1st train = x and of 2nd = y.
when they cross man then.....
so length of 1st = 27x and second 17y.
total length = 27x + 17y
now when they cross each other in opp direction they take 23 sec and we know when 2 object run in opp direction their rel speed is
speed of 1st + speed of 2nd = x+y so now length = time * speed = 23(x+y)

Compare both :
27x + 17y = 23(x+y)
27x + 17y = 23x + 23y
4x = 6y => x/y = 3/2.

Let Speed of Train A= x m/s
And Speed of Train B= y m/s

Time taken by Train A to cover distance equals to its length = 27 s

Time taken by Train B to cover distance equals to its length = 17 s

Total distance covered
---------------------- = Time taken to Cross each other
Total speed


(Length of train A)+ (Length of train B)
so, --------------------------------------- = 23 seconds
(Speed of train A) + (Speed of train B)

(Speed x time) of Train A + (Speed x time) of Train B
----------------------------------------------------- =23
(Speed of train A) + (Speed of train B)

27x + 17y
--------- = 23
x + y

27x + 17y = 23x + 23y
4x =6y

x/y= 3/2

I can't get this step

(27x+17y) / (x+y) = 23

Why we have to use this? can any one explain me.

I think I am contented with fathima explanation thank you all.

The 1st train sec 27-23=4.

The 2nd train sec 23-17=6.

So both are divide by 2.

4/2=2, and 6/3=3.

So the ratio is 3:2 its right method?

@ chanti
its length=speed*time
so length of first train=27*x mts
and length of 2nd train= 17*y mts

Hi friends in smart way....

To find out the speed ratio so ,

formula is Length = speed*time
so,

speed = length /time

here 2 trains so two different length and speed so the formula

s1+s2=L1+L2/time

speed we don't know so we take X,Y for speed for 2 trains
respectively ....
use above formula:

X+Y=L1+L2/23

HERE
L1=speed*time (speed is not given so take it as X,time is given that is 27)

L2= speed*time (speed is not given so take it as Y,time is given that is 17)
SO L1=27X
L2=17Y
apply it,
X+Y=27X+17Y/23

SO SOLVE IT
23(X+Y)=27X+17Y
23X+23Y=27X+17Y

separate the X and Y terms so we get

23X-27X+23Y-17Y=0

WE GET:
-4X+6Y=0
6Y=4X

RATIO (means difference of X and Y)
SO FRIEND,

X/Y=6/4=3/2
SO THE RATIO IS 3:2