Aptitude - Problems on Trains - Discussion

@Narayana superb.

Let the speed of the train is Xm/s & Ym/s resp.
accordingto the qus.
27x meter is the speed of the first train
17x " " " second "
finally both the the train meet =23(x+y)
27x+17y=23(x+y)
4x=6y
x/y=3/2

Speed=distance*time or length*time
Speed of the first train=X*27
Let X=distance of first train
Let Y=distance of second train
Speed of the second train=y*17
If train moves in opposite direction means total speed is addition of two train speed
27X+17Y

Both trains meet in 23 second by crossing a man
1'st train speed=23X
2nd train speed=23Y
Total speed=23X+23Y

So first train speed =(27-23)*X
2nd=(23-17)*Y

Equating both speed 6X=4Y

X/Y=6/4=3/2.

If 2 Train are moving in opposite direction(train a 27 & train b 17)then Formula applied is

The time taken by the trains to cross each other( 23 )given =(a + b)/(u + v)sec.

* 27u + 17v = 23
-----------
u + v

* 27u + 17v = 23u + 23v

* 27u - 23u = 23v - 17v

* 4u = 6v

* u/v = 6/4

* 3:2 is the answer.

Here concept of relative velocity is used.

When objects move opposite to each other, their speed is added and when they move in same direction speed is the difference of their respective speeds.

Given data:

l1=27 m/s.
l2=17m/s.

Now, we can find speed
s=l/t .

But speed is not given consider speeds x and y.

Now easy to find lengths,
l1=t*s =27x
l2=t*s =17y

If two trains travelling in opposite directions then we add two lengths(l1 and l2) and x and y speed m/s so that we able to find ratios.

Now the time taken by train to cross each other is given i.e 23 seconds.

Now formula forms like this :

( l1 + l2)
---------- = 23.
( x + y )

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

(27x - 23x ) = ( 23y - 17y ).

(4x)=(6y).

x 6 3
-=-=-
y 4 2

When two train s of a length a and b, of speed u, v m/sec.they move to cross each other. Time taken by the two trains cross each other is a+b(u+v). Because of these formula we have find the length of trains. I hope understood these problem.

Hai every body,
The speed of one train = x, Speed of another train = y.
We know that speed = length/time || length = speed*time.

So we find the length of the first train = x(speed)*27(time).

The length of the second train = y(speed)*17(time).

Time taken by both train to cross(total time) = 23.

Total length = (length of the first train)+(length of the second train) = (x*27)+(y*17).

Total speed = (speed of first train) + (speed of the second train) = x+y.
Total time = total length/total speed.

23 = [(x*27)+(y*17)]/(x+y).
27x+17y = 23(x+y).
27x+17y = 23x+23y ||27x-23x = 23y-17y || 4x = 6y ||x/y = 3/2.

@Faty how can you say total speed is (x+y). Duh the train are moving in different direction. So their total speed need to be (x-y) according to your point of view.

@Hardik Mistry : When trains move in opposite direction their speeds are added, but when they go in the same direction their speeds are subtracted. Imagine you are going on road by bike and another bike is coming from front (i. e opposite direction) , you feel that the other bike is coming faster. But if it comes from back and tries to overtake you (i.e same direction) then it overtakes you slowly as compared to its speed.