Aptitude - Problems on Ages - Discussion

Given:

Father age = more than 3 times son age.
After 8years = more than 2 1/2 time son age.
After 8 years = more than 2-time son age.

Every 8 years 1/2 times reduced.

@All.

Simply, the solution is;

Given:

Ist father age= 3 times more than son age.
2nd after 8yrs father age= 2 1/2 times more than son age.
3rd after 8 yrs age =2 time more than son age.

As they said that father age is thrice,hence;

Let father present age = x,
Ronith age = y,

X = 3 * Y. => Y=X/3.

In the 2nd part, they mentioned that aftr 8yrs father age is 2.5 times of his son's age, hence
(X+8)=5/2(Y+8).

By substituting y=X/3, we get father present age i.e X=72yrs, Y=24yrs.

Then again he asked that how many times the difference between father and sons age further 8 yrs later;
Say later 8 yrs their difference is z. Hence
(X+8)=z(Y+8).

Putting X=72 and Y=24.
Then we get the difference is as z=2(approximately).

Let son age be x.

Father's age is 3 times more than son's age.
Which means x+3x=4x.
After 8years.
X+8=2 and half of x.

When we solve the equation we will get x as 8.
4x=32,

In the beginning of the question state that father's age is 3 times more than son age.
So x=8 then 3x=24.
After further 8years it becomes,
32+8=40.
3*8=24 and 5*8=40,
3-5=2.
and 2 times.

For every 8 years father's age decrease by halftime of his son's age so after further 8 years (5/2) - (1/2) =2 times.

How last step 4x+16/x+16?

Can't we take 2.5 instead of 5/2?

How comes 5/2? please explain.

How this ratio came into picture 4x+8?

How come 4x+16/x+16 = 48/24? Anyone explain me.