# Five years ago twice the age of father is equal to 8 times that of the son’s age, two years from now half the sum of ages of father and son is 32, fin

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Five years ago twice the age of father is equal to 8 times that of the son’s age, two years from now half the sum of ages of father and son is 32, find the age of father when child was born?
1. 35 yr
2. 30 yr
3. 40 yr
4. 29 yr
5. 32 yr

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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.