Aptitude - Problems on Ages - Discussion

How can you subtract the past age of father from his present age to get get the present age of son? I can't get you.

Reading which part of the question I should go for making this equation 38-x = x.

38-x age of father at born time.

Here is the clarity:

Let present age of son = x.

Given father present age = 38.

According to logic when son age is 0 (during birth), fathers age is x.

Then when son's age is x, then father's age is 38.

So x-0 = 38-x.
2x = 38.
x = 19.

Then 5 years back of son's age it will be 14 years.

Hope you understood.

"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.

How can we use same variable for both son's present age and father's age at the time of birth?

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.

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.

It means father's age at the time of his son's birth is equal to son's age at present.

If we take sons age at present as "x" father's age at his son's birth is also "x".

So, 2x = 38.

x = 19.

How did the relation 38 - x = x arise? Explain it.