Aptitude - Problems on Trains - Discussion

Let speed of train1: x m/s.
Speed of train2: y m/s.

Then relative speed of train1 = (x+y) m/s............(1).

Train are crosses a man means they cross their length.

Length of train1: 27x m.
Length of train2: 17y m.

According to Qst:

Train crosses Each other in 23sec.
Means train1 crosses his length & also the length of train2.

=> Total length crosses by train1 = Length of train1+Length of train2.
=>Total length covered by train1(D)=27x+17y...........(2).

We knows,

Speed(s) = Distance(D)/Time(t)............Eqn(3).

Put Values OF eqn(1) &(2) in eqn(3).

x+y = (27x+27y)/23.
=> 23x+23y = 27x+17y.
=> 27x-23x = 23y-17y.
=> 4x = 6y.

=> x/y = 6/4 = 3/2..........Answer.

Very short form is:

(27-23):(23-17),
4:6,
2:3.

So the ratio is 2:3 or 3:2.

I have solved it in yet simple(crude) way.

Don't worry about their crossing each other in 23 seconds or whatever.

On the face of it, one can make out that he has asked the simplified ration for 27:17.

Simply take them to next higher level so that both of them are divisible by common highest divisor.

i.e. 30/20 = 3/2.

(but recommended not to follow it, as it doesn't apply to every problem?).

SPEED = DISTANCE/TIME.

DISTANCE/SPEED = TIME.

i.e 27X+17Y/X+Y = 23.

@Arashan has describe very well with formula of speed.

Lets assume,

The train 1 speed= x m/sec ==> distance traveled by the train 1= 27*x m.
Similarly assume the speed of the train 2 is y m/sec then the train 2 has traveled a distance of 17*y meter.

The total distance (x+y)*23 m.

Therefore,

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

Therefore x:y= 3:2. Answer B.

Hey if we follow the physics concept then relative distance should decrease while crossing each other. Then it should be (27x - 17y)/(x+y). Isn't it?

Why should both trains have different length. Even sometimes they can have same length and can run in different speeds right. Then how can we do like that. Can anyone explain please?

If I divide speed of one train 27 divided by another its almost 1.5 can I choose 3:2. Is it a pure coincidence ?

#Vivek kumar.

Here the questions is : two train of length a and b are run in opposite directions at u m/sec. and v m/sec., then the time taken by the trains to cross each other = (a+b)/(u+v).

And if two train of length a and b are run in same directions at u m/sec. and v m/sec., then the time taken by the faster trains to cross the slower train = (a+b)/(u-v)