Aptitude - Problems on Trains - Discussion

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

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

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

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

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)

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

Since both the trains are moving in opposite direction. To find total we have to add the sum of train length.

Sorry guys for pecking on the same thing again.

But Why is it necessary that total distance covered = sum of the train's length?

Isn't the above question assuming that before the collision both trains are travelling the distance only equal its own length.

Excellent explanation SRI.

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:

Relative speed of the trains =x+y(since they are moving in opp direction)

Total distance covered = L1+L2
So time taken to cross each other = total distance /relative speed

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