Aptitude - Problems on Ages - Discussion

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.

As it is said that father's age is 3 times more than his son's.

So father's present age 3x and son's age x.
After 8 yrs their age will be,
3x+8 = 5/2(x + 8),
3x+8 = ((5x)/2) + (40/2),
2 * (3x+8) = 5x + 40,
6x + 16 = 5x + 40,
x = 24.

So son's age will be 24.
And father's age will be 3x = 72.

Further 8 more years ie; after 16 years,
Son's age will be x+16 ie; = 40,
and father's age will be 3x+16 ie; =88,

Therefore (x+16) ÷ (3+16) = 2.2.

Let the age of son be x then age of father will be 4x so we have ratio of father and son equals to 4x:x again after 8 years this becomes 5/2x:x as we all know that difference of age remains same then to make it same multiply above by 2 so that it becomes 5x:2x.

Therefore in 8 years 4x becomes 5x hence x is equal to 8 putting the value we get the age equal to 40 and 16 respectively and after 8 more years it will become 48 and 24 and hence father's age will be twice of the son.

I think 2.5(x+16) = (4x+16).

@Amrutha.


The correct answer is 11:5.

Fathers present age :72
Son's present age :24
So ratio:- 3:1

After 8 years:
father's age: 80
son's age: 32
so ratio:- 5:2

Further 8 years after:
Father's age : 88
Son's age: 40
So ratio : 11:5 is the correct answer.

Son- x father- 3x BUT, it is said MORE than 3 times so x +3x= 4x.

Now, 8 years ahead, son= x+8 and father= 5/2*(x+8).
---> (x+8)=5/2*(x+8),
---> 2(x+8)=5(x+8),
---> 2x + 16= 5x + 40,
---> x= 8 - sons age.
father is 4x= 4*8= 32.

NOW, in total 16 years is asked from the beginning,
So, sons age= 8+16= 24,
Fathers age= 32+16= 48,
48 is 2 times of 24!.

(4x+8) = 5/2(X+8).
= 8x+16 = 5x+40 how it came?