Five years ago a woman's age was the square of her son's age. Ten years hence her age will be twice of her son's age. find i) the age of the son five years ago ii) the present age of the women.
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Solution
Let Son's age = x
Let Women's 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]