Aptitude - Problems on Trains - Discussion

27x+17y
-------- = 23
x+y
27x+17y=23x+23y
27x-23x=23y-17y
4x=6y
3 x
- =- x:y= 3:2
2 y

By the formula time=distance/speed.

but, we have two trains with two diferent distances and speeds.

then we use the formula,

total time = [(distance1)+(Distance2)]/[speed1+speed2]

for finding distance= speed*time.[so,distance1= 27*x....like wise.

finally we get, 27x+17y/(27+17)= 23 (given totaltime.)

at last the answer is... x:y (3:2)

Can anyone how we got 3/2 since I understood till 4x=6y after that I didn't get that division step.

hi nayana wen u cud understand till 4x=6y then wats complex there just bring y and 4 to the opp side then x/y=6/4
cancel by gcd thats it get the solution 3/2

Thank u sumi i was confused in that step now i got..

When u refer the important formula we can come to know that "Time taken by a train of length x metres to pass a pole or a signal post is equal to the time taken by the train to cover x metres"

This theorem indirectly show us that the length of the train is 27 metres and 17 meters respectively ok

Then according to the 8th formula that "If the train of length a metres and b metres are moving in the opposite direction at u m/s and v m/s then the time taken by the trains to cross each other = a+b/u+v sec
we don't know the value of u and v so let take it as x and y
then:
a=27x
b=17y
therefore 27x+17y/x+y = 23

take x+y to the right side though it is in division it will turn to multiplication
like this:
27x+17y = 23(x+y)
27x+17y = 23x+23y
then calculate difference between x and y
you will get 4x = 6y
2x = 3y
and x/y = 3/2

I didn't understood why x+y is divided by the term 27x+17y... can any body help to explain clearly

As we know that,when two train of length l1 and l2 travels in opposite direction with speed let s1 km/hr and s2 km/hr respectively then time taken to cross each other is given by formula

t=(l1+l2)/(s1+s2)

So by using this formula we can easily solve the above problem.

here l1=27*s1=27s1.
l2=17*s2=17s2.

and t is given in problem equal to 23.

therefore,
23=(27s1+17s2)/(s1+s2)=>3:2

Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:.

Its given as Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds.

So it should be taken as 27x and 17x seconds only, I don't know why it is given as 27x and 17y meters and also denoted as length of train. Please any one explain me?

X+Y is speeds of 2trains and 27x+17y is length of trains
so lenth/speed=time