Question

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

Answer 1

Given:

✭ Age of a man = Twice the square of the age of his son

✭ Age of man after 8 years = 4 more than 3 times son's age then

To Find:

The present age of father and son

Solution:

Let

• The age of the man be x years
• The age of son be y years

Hence by given,

⪼ x = 2y² -eq(1)

Age of man and son after 8 years will be,

»» Age of man = x + 8

»» Age of son = y + 8

By given,

➢ x + 8 = 4 + 3 (y + 8)

➢ x + 8 = 4 + 3y + 24

Substitute value of x from equation 1

➝ 2y² + 8 = 4 + 3y + 24

➝ 2y² + 8 = 3y + 28

➝ 2y² - 3y - 20 = 0

Factorising by splitting the middle term

›› 2y² - 8y + 5y - 20 = 0

›› 2y (y - 4) + 5(y - 4) = 0

›› (y - 4) (2y + 5) = 0

›› 2y + 5 = 0

›› 2y = -5

›› y = -5/2

This can't happen since age can't be negative

➠ y - 4 = 0

➠ y = 4

Hence age of son = 4 years

Substitute the value in equation 1

➳ x = 2 × 4²

➳ x = 2 × 16

➳ x = 32

∴ Hence father's age is 32 years & Sons is 4 years old.

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Answer 2

$\huge\underline\bold\red{Solution}$

Assume :-

• The age of the man be x years

• The age of son be y years

Hence ,

- x = 2y² from equation 1

Age of man and son after 8 years will be :-

• Age of man = x + 8

• Age of son = y + 8

By given,

• x + 8 = 4 + 3 (y + 8)

• x + 8 = 4 + 3y + 24

$Putting \: the \: value \: of \: x \: from \: equation \: 1$

$\dashrightarrow$ 2y² + 8 = 4 + 3y + 24

$\dashrightarrow$ 2y² + 8 = 3y + 28

$\dashrightarrow$2y² - 3y - 20 = 0

$\small\underline\bold\red{Factorising\: by \:splitting \:middle\: term }$

$\implies$2y² - 8y + 5y - 20 = 0

$\implies$2y (y - 4) + 5(y - 4) = 0

$\implies$(y - 4) (2y + 5) = 0

$\implies$2y + 5 = 0

$\implies$2y = -5

$\implies$y = -5/2

Age can't be negative

$\implies$y - 4 = 0

$\implies$y = 4

Hence age of son = 4 years

putting the value in equation 1 :-

$\implies$x = 2 × 4²

$\implies$x = 2 × 16

$\implies$ x = 32

$\large\underline\bold\blue{Final \: Answer }$

$\implies$ father's age is 32 years and Son's is 4 years old .