the sum of Ages is a man and his son is 45 years. five years ago the product of their ages is equal to the 4 times of his father age at that time the age of father and the son respectively
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Let the age of father be x years.
So, Age of son will be ( 45 - x ) years.
Five years ago,
Age of father = x - 5
Age of son = 45 - x - 5 = 40 - x
ATQ,
( x - 5) ( 40 - x ) = 4 ( x - 5 )
40x - x^2 - 200 + 5x = 4x - 20
-x^2 - 200 + 45 x = 4x - 20
0 = x ^2 + 200 - 45 x +4x - 20
0 = x ^2 - 41x + 180
0 = x^2 - 36x - 5x + 180
0 = x ( x - 36) - 5 ( x - 36 )
0 = ( x - 5) ( x - 36 )
x = 5, 36
So, Age of father = 36 years
Age of son = ( 45 - 36 ) = 9 years.
So, Age of son will be ( 45 - x ) years.
Five years ago,
Age of father = x - 5
Age of son = 45 - x - 5 = 40 - x
ATQ,
( x - 5) ( 40 - x ) = 4 ( x - 5 )
40x - x^2 - 200 + 5x = 4x - 20
-x^2 - 200 + 45 x = 4x - 20
0 = x ^2 + 200 - 45 x +4x - 20
0 = x ^2 - 41x + 180
0 = x^2 - 36x - 5x + 180
0 = x ( x - 36) - 5 ( x - 36 )
0 = ( x - 5) ( x - 36 )
x = 5, 36
So, Age of father = 36 years
Age of son = ( 45 - 36 ) = 9 years.
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