Question

the age of aman is twice the square of the age of his son. Eight years hence,the age of the man will be 4 years more than three times the age of his son .find their present age

Answer 1

Hi !

Age of son = x years

given ,

Father's age = 2(x²)
= 2x²

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ages after 8 yrs ,
Aman's age = 2x² + 8 yrs
Son's age = x + 8 yrs

Given ,
2x² + 8 = 3(x+8) + 4

2x² + 8 = 3x + 24 + 4

2x² - 3x = 28 - 8

2x² - 3x = 20

2x² - 3x - 20 = 0

factorizing by splitting the middle term :-

2x² -8x + 5x -20 = 0
2x(x - 4) + 5(x-4) = 0

(x-4) (2x+5) = 0

x = 4 , x = -5/2

we are taking x = 4 , as age cannot be negative.

Age of son = 4 years

father's age = 2x² = 2 × 4² = 2 ×16
= 32 yrs

Answer 2

hope this helps u



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