Question

Five years ago, a woman's age was the square of her son's agem Ten years hence, her age will be twice that her son's age.
Find:
1) the age of the son five years ago.
2) the present age of the woman.​

Answer 1

Answer:

let the son's age be x

1) x+10

2) 2x

Step-by-step explanation:

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Answer 2

❍ Let the age of the son 5 years ago be x years, then the age of the woman 5 years = x² years.

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∴ The present age of the son = (x + 5) years

and the present age of the woman = (x² + 5) years.

• Ten years hence i.e. after 10 years from now,

⁕ the age of the son = { (x + 5) + 10} years = (x + 15) years.

and the age of the woman { (x² + 5) + 10} years = (x² + 15) years.

★ According to given, x² + 15 = 2 (x + 15)

➬ x² + 15 = 2x + 30

➬ x² - 2x - 15 = 0

➬ (x - 5) (x + 3) = 0

➬ x - 5 = 0 or x + 3 = 0

∴ But, x being age cannot be negative.

➬ x = 5

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① The age of the son 5 years ago = 5 years.

② The present age of the woman = (x² + 5) years

= (5² + 5) years

= 30 years.

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