Question

Paul is x years old and his father's age is twice the square of Paul's age . Ten years hence , father's age will be 4 times Paul's age. find their present ages .
 

Answer 1

Let,

Pauls's present age be x.

So his father's age will be 2(x²)

A/Q,

2x² +10 = 4(x+10)

2x² + 10 = 4x + 40

2x² - 4x = 40-10

2x² -4x = 30

2x² -4x - 30 = 0

2x² - 10x + 6x - 30 = 0

2x(x-5) + 6(x-5) = 0

(2x + 6) (x-5) = 0

2x + 6 = 0  or  x - 5 = 0

2x = -6     or x = 5

x = -6/2  or x = 5

x = -3  or  x = 5

So x = -3, 5

So the age should be in negative value therefore present age of paul is 5 years and his father's age 2(5)² = 2 x 25 = 50 years.

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