Question

The age of a man is twice the square of the age of his son. Eight years hence, the age of the man will be 4 years more than three times the age of his son. Find their present ages.​

Answer 1

Answer:

Son=4 yrs

Father= 32yrs

Step-by-step explanation:

Let age of father be x and son be y.

Then,

$x =2 y ^{2}$

$x + 8 = 3(y + 8) + 4$

Now solve.

Answer 2

Answer:

• Age of man is 32 year and age of son is 4 year.

Step-by-step explanation:

GIVEN INFORMATION :-

• The age of a man is twice the square of the age of his son.
• Eight years hence, the age of the man will be 4 years more than three times the age of his son.

TO FIND :-

• Present age of man and his son.

SOLUTION :-

Let the present age of son is x years

Then

↝ According to First information -

The age of a man is twice the square of the age of his son.

$\sf \: The \: \: age \: \: of \: \: a \: \: man = twice \: \: the \: \: square \: of \: \: son$

$\sf \: The \: \: age \: \: of \: \: a \: \: man = 2 {x}^{2}$

↝ According to Second Information.

$\sf \: ↝ \: 8 \: years \: hence \: -$

$\sf \: Age \: \: of \: \: son = (x + 8) \: year$

$\sf \: Age \: of \: man \: = (2 {x}^{2} + 8) \: \: year$

The age of the man will be 4 years more than three times the age of his son.

$\sf \: the \: \: age \: \: of \: \: the \: \: man = 4 \: year \: more \: than \: \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: three \: times \: the \: son$

$\sf \: (2 {x}^{2} + 8) = 4 + 3(x + 8)$

$\sf \implies \: 2 {x}^{2} + 8 = 3x + 24 + 4$

$\sf \implies \: 2 {x}^{2} + 8 = 3x + 28$

$\sf \implies \: 2 {x}^{2} - 3x - 20$

$\sf \implies \: 2 {x}^{2} - 8x + 5x - 20$

$\sf \implies \: 2x(x - 4) + 5(x - 4)$

$\sf \implies \: (x - 4)(2x + 5)$

Hence

$\sf \implies \: x = 4 \: \: or \: \: \frac{ - 5}{2}$

but age can't be negative

$\sf \: hence \: \: \boxed{ \sf x = 4}$

Age of son =x = 4 years

$\sf \: Age \: \: of \: \: man = 2 {x}^{2}$

$\sf \: Age \: \: of \: \: man = 2( {4}^{2})$

$\sf \: Age \: \: of \: \: man = 32 \: year$