# Five years ago, a woman’s age was the square of her son’s age. Ten years hence her age will be twice that of her son’s age. Find : (i) The age of the son five years ago (ii) The present age of the woman.

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Let Womens age = y

y - 5 = (x - 5)² -------------1

y + 10 = 2(x+10)----------2

Equation 1

y - 5 =x² - 10 x + 25

y = x² - 10x + 30

Equation 2

y = 2x +10

Substituting The Value Of y in equation 1

2x + 10 = x² - 10x + 30

x² - 10x - 2x + 30 - 10 = 0

x² - 12x + 20 = 0

x² - 2x - 10x + 20 = 0

x(x - 2) -10(x - 2) = 0

(x - 10)(x - 2) = 0

x = 10 or x = 2[ x cant be 2 as five years ago it would be negative age]

y = 20 + 10

y = 30 yrs