Aptitude - Problems on Ages - Discussion

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

How this ratio came into picture 4x+8?

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

How comes 5/2? please explain.

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

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.

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.

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).

@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.

Father age can be taken as x.
Son age is taken as y.

According to the first statement, father age is three times more than sons age at present is x=3y

According to the second statement after 8 years father age is 8 times more than the two and a half age of son age.

2*1/2 can be written as 5/2.
So, x+8=5/2y.
Substitute x=3y,
3y+8=5/2y,
3y-5/2y=-8,
1/2y=-8.
y=-16 after 8 years.
After 8 years father age is twice than son age.
Then after 16 years also twice than son ager.