Aptitude - Problems on Ages - Discussion

Fathers current age is 38, since we don't know son's age we will consider his age as X. So now,

Fathers current age is 38--------------------(eqn 1).

Sons current age is X.

When his son was born then his fathers current age should be X(because "I was as old as you are at the present at the time of your birth")(sons present age is X, so when father told this dialogue then at that time his age should also be X).

So at the birth sons age is 0 and his fathers age is X.
During Birth:

Son's current age = 0.
Fathers current age = X.

Now son has grown upto X years so father will also grow up to X years, so Sons age will be 0+X and fathers age will be X+X.

Fathers age =X+X=2X-----------------------(eqn 2),

Equating (1)&(2),

2X = 38.

X = 19.

Sons current age is 19 and 5 years back he will be 19-5 = 14.

1. If at the time of father's age @15 years, his son was born, at that time son age is @1 year.

If father come into age @30 years, his son age is @15 years.

2. If at the time of father's age @20 years, his son was born, at that time son age is @1 year.

If father come into age @40 years, his son age is @20 years.

3. If at the time of father's age @19 years, his son was born, at that time son age is @1 year.

If father come into age @38 years, his son age is @19 years.

Finally that 19 years is present age of son.

But they are asking 5 years ago so, 19 years - 5 years = 14 years.

Son's age would always be half of father's age no matter what the father age is !

Because let say son age is 'x' now. When son born father age is also 'x'. So when son grew up and reach 'x', now father would be 2x.

So to find son age just divide fathers age by 2 (2x / 2 = x (son age) ).

Simple example: let say father age is 40.

0 x 20.
Son = <---------------->.
0 x 20 x 40.
Father= <-----------------><--------------->.

Then son ages - 5 = answer.

@Siva.

In the question, "I was as old as you are at the present at the time of your birth"
Son's present age = Father age when son was born.

In the question father age=38, let son age be 'x'.
Father present age - son present age = father age when son was born ( i.e., son present age)
38 - x = x.
38 = 2x.
x = 19.
Sons age 5 years back x-5 = 19-5 ==>x = 14.

How did we know that the father's age is now double of son's age?

As @Naseem has mentioned. How can the mere mention of a father proclaiming that "he was the same age as the present age of the son, at the time of son's birth". Indicate or point out that the father's present age is double of the son, or that the son's age is half of the father. This is the greatest unsolved mystery of this question that has been in my mind for years.

From solution we found that, x = 19 i.e. son's present age.

Father's present age = 38.

Given statement: "I was as old as you are at the present at the time of your birth".

i.e age of father when his was born.

Hence, Father's present age - Son's present age.

= 38-19 = 19. Father's age at the time of his son's birth.

And son's present age + Father's age at the time of his son's birth.

i.e 19+19 = 38. Its prove check it out.

Hi Friends,

In the question itself it is clearly said Son's Present age is same as Father age at the time of his son's birth.

So sons age will be half the age of father at any time.

So if sons age is x, then father age is 2x.

Given father present age is 38, so obviously son's present age will be half of father's hence sons age is 38/2 which is 19 years.

Sons age before 5 years is 19-5=14.

@All.

Here is a simple way to understand this:

f = 38 (f for father's age),
x = son's age today.
x = number of years passed since the son was born until today (same thing in different words)
x = the age of the father when the son was born.

The age of the father when the son was born + the number of years passed since the son was born = the father's age.

x + x = 38.
2x = 38,
x = 19.

"I was as old as you are at the present at the time of your birth" means that at the time of son birth father age was equal to present son age. So father age is now double of son age. Father's age now 38 year.

If son age is x then father's age = 2x.

Given that father's age = 38.

So, 2x = 38.

=> x = 19.

5 year back is x-5.

i.e 19-5 = 14.

Father Son.

Present age -> 38 let be 'x'.

At Birth -> 38-x (x-x) = 0.

By statement: I was means father was was as old as you as you are at the present i.e. son at the time of son's birth so,

Present age of son = x years.

Fathers age at son's birth = (38-x).

Just equate it: x = 38-x.

x = 19.

They want 5 years ago so 19-5 = 14.