Question

3 years ago the age of a man is the square of the age of his son. 6 years hence the age of the man will become thrice the age of his son. find present age of man and age of son three years ago

Answer 1

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Answer 2

Let the present age of man be x years and his son's age be y years.
Three years ago,
Man's age = ( x - 3 ) years
His son's age = ( y - 3 ) years
Given :
( x - 3 ) = ( y - 3 ) ( y - 3 )
x - y^2 + 6y = 12 ........................(i)
Six years hence,
Man's age = ( x + 6 ) years
His son's age = ( y + 6 ) years
Given :
( x + 6 ) = 3 ( y + 6 )
x + 6 = 3y + 18
x - 3y = 12 .....................(ii)
Now, By substitution method
From eq (ii) we have,
( x = 12 + 3y ) .........................(iii)
Put this value in eq (i)
x - y^2 + 6y = 12
12 + 3y - y^2 + 6y = 12
12 + 9y - y^2 = 12
9y - y^2 = 0
9y = y^2
( y = 9 )
And, Put the value of y = 9 in eq. (iii)
x = 12 + 3y
x = 12 + 3 x 9
x = 12 + 27
x = 39.............Answer

Hence, the present of Man is 39 years.
the age of son three years ago is ( y - 3 ) = 6 years.