Correct Answer - Option 2 : 30 yr

**Given****∶**

Five years ago twice the age of father is equal to 8 times that of the son’s age.

And two years from now half the sum of ages of father and son is 32.

**Concept used :**

Here we will be using the basic concept of ratio.

**Calculation****∶**

Let the present ages of father and son be F and S respectively.

Age of father five years ago be = (F - 5)

Age of son five years ago be = (S - 5)

Ages of father and son two years from now will be (F + 2) and (S + 2) respectively.

According to question;

⇒ 2 (F - 5) = 8 (S - 5)

⇒ 2F - 8S = - 30 ---(1)

And,

[(F + 2) + (S + 2)] / 2 = 32

⇒ F + S = 60 ---(2)

On solving equations (1) and (2), we get, F = 45 and S = 15

⇒ present age of father = 45 years and present age of Son = 15 years

So age of father at the time of son’s birth = 45 - 15 = 30 years

Hence the age of father at the time of son’s birth is 30 years.