Aptitude - Problems on Trains - Discussion

Step (1)
Speed= (Distance/Time) meters/sec. Distance= Length here.
From this formula, Length = Speed* Time

So,Length of 1st Train= Speed * Time = 27* x where x=speed
Likewise,length of 2nd Train .= 17* y where y=speed

Step (2):
Note:Imagine one train is stationary. Then the distance traveled by each train would be equal to the length of the other train + its own length.Because a train can cross the other train after the last bogie of the 1st train crosses the last bogie of the other train.
So total length of both trains = 27x+17y.
Now the relative speed of the trains = x+y (since both run in opposite directions).

So Time = Length/speed= 27x+17y/x+y =23(given)
Cross multiply,transpose and simplify. Then you get the answer.

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