Aptitude - Problems on Trains - Discussion

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

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.

A = 27 - 23sec = 4sec.
B = 23 - 17sec = 6sec.
A:B = 4:6 = 2:3 in Sec.
A:B = 3:2 in Speed.

Your answer is wrong; the final answer is (D) none of these.

Because X is the upper side and Y is the lower side, and the ratio is 2:3, not 3:2.

I can't get this step

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

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

Anyone please help me how this x+y is divided.

(27x+17y)/x+y=23 how did used that step?

It's correct method to solve this problem.

very good solution....

Based on the below formula -- >

If two trains of length a(i.e. 27x) metres and b(i.e. 17y) metres are moving in opposite directions at x m/s and y m/s, then:

The time taken by the trains to cross each other (i.e.23 sec) =

(27x + 17y)
```````` secs
(x + y)


Therefore, the above solution is provided based on this derivation. Its given in the formulas section.