Aptitude - Problems on Ages - Discussion

38-x = x? Can any one explain in detail?

Please explain confidentially.

Don't write "x" just place the numbers the alphabetical symbols are quit disturbing.

How can we say that Both X is same variable?
I mean why 38-X = X,

Why not 38 - X = Y, where Y is Father's age.
At the time of Son's birth.

Father current year 38.

Son age consider x.
The sons age = father's.
Age at the time son's birth.

Father's present age - Son's age = Father's age
At the time of Son's birth.

38-x = x.
38 = x+x.
38 = 2x.
x = 38/2 .
x = 19.

Son's age 5 years back (x-5)=(19-5)=14 is correct answer !

I still not got exact intelligible meaning of that sentence told by father.

Father's age now is 38; let son's age be x.
Son's current age = age of his father on his birth.i.e. x.

If we subtract son's current age from father's current age ie x=(38-x).
We get father's age @ the time of son's birth which is x.

And we observe father's age @the time of son's birth = x = son's current age.
38-x = x.

Father's age (38-x).

Son's age x.
Son's age before 5 years (x-5).

Father's age before 5 years (38-x) -5.

(38-x) -5 = (x-5).
33-x = x-5.
33+5 = x+x.
38 = 2x.
x = 19.

Therefore son's age before 5 years (x-5) = (19-5) = 14.

Let the son's present age be x years. Then, (38 - x) = x. -> why x is subtracted from 38?

2x = 38. -> how 2x = 38 its not mentioned in the question?

x = 19.

Son's age 5 years back (19 - 5) = 14 years.

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.