Aptitude - Problems on Trains - Discussion

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

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.

Given:
1. time taken by the first train to cross a man (t1) = 27 sec
2. time taken by the second train to cross a man (t2) = 17 sec

3. Time taken by the 1st & 2nd train to cross each other (T)= 23 sec

Find: Ratio
1st train's speeds (x) / 2nd train's speed (y) = x/y = ?

Formula:

speed =
distance(or length)
---------------------
time

Let,
Speed of 1st train to cross a man (x) = distance(d1) / time(t1)
Speed of 2nd train to cross a man (y) = distance(d2) / time(t2)

Thus,
x = d1/27 .................I
y = d2/17 .................II

So, Total speed of the train (S) = speed of 1st train (x) + speed of 2nd train (y)
Therefore, S = x + y

Now, we can say that
Total distance (D) = d1 + d2
D = 27x + 17y............from I & II

Total time (T) = 23 seconds

Total speed of the train (S) = Total distance (D) / Total time (T)

x + y =

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

23x + 23y = 27x + 17y
23y - 17y = 27x - 23x
6y = 4x
x/y = 6/4 = 3/2
Thus,
1st train's speeds (x) / 2nd train's speed (y) = x/y = 3/2

Let the speeds of the two trains be x m/sec and y m/sec respectively.

Then, length of the first train = 27x metres,(length=speed*time..so length=x*27=27x metres)

And length of the second train = 17y metres.(length=speed*time..so length=y*17=17y metres)

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.
By using above formula we get d solution for this.
Here it is given that they cross each other in 23 seconds.
So

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

23x + 23y = 27x + 17y
23y - 17y = 27x - 23x
6y = 4x
x/y = 6/4 = 3/2
Thus,
1st train's speeds (x) / 2nd train's speed (y) = x/y = 3/2.

@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