Question

The age of the father is 6 times the age of the son. After four years his age will be 4 times the age of the son. What will be his present age...​

Answer 1

$\textsf{\large{\underline{Solution}:}}$

Let the present age of son be x years. So, the present age of father will be 6x.

After 4 years:

$\sf\implies Age\ Of\ Son = (x + 4)\ years.$

$\sf\implies Age\ Of\ Father = (6x + 4)\ years.$

According to the condition given:

$\sf\implies Father's\ Age = 4\times Son's\ age$

$\sf\implies 6x+4=4(x+4)$

$\sf\implies 6x+4 = 4x+16$

$\sf\implies 6x-4x = 16-4$

$\sf\implies 2x = 12$

$\sf\implies x = 6$

Therefore, the present age of son is x years i.e., 6 years.

So, the father's age will be 6x years i.e., 36 years.

$\textsf{\large{\underline{Verification}:}}$

Father's age is 6 times the age of son - Verified.

After four years, son's age will be (6 + 4) years or 10 years and similarly, father's age will be (36 + 4) years i.e., 40 years which is four times the age of son.

Hence, verified.

$\textsf{\large{\underline{Final Answer}:}}$

1. Present age of son = 6 years.
2. Present age of father = 36 years.