The present age of father is equal to the square of the present age of his son. One year ago, the age of father was 8 times the age of his son. Find their present age.
Answers
Answer:
Present age of son is 7 years.
Present age of father is 49 years.
Step-by-step explanation:
Let,
Present age of son be a years.
So, present age of father should be a^2 years, since age of father is square of the age of son.
One year ago : Age of father was 8 times the age of his son.
= > Age of father that time = 8 x age of son that time
= > Present age - 1 year = 8 x ( present age - 1 year )
= > a^2 years - 1 year = 8( a years - 1 year )
= > a^2 - 1 = 8( a - 1 )
= > a^2 - 1 = 8a - 8
= > a^2 - 8a + 8 - 1 = 0
= > a^2 - 8a + 7 = 0
= > a^2 - ( 7 + 1 )a + 7 = 0
= > a^2 - 7a - a + 7 = 0
= > a( a - 7 ) - ( a - 7 ) = 0
= > ( a - 7 )( a - 1 ) = 0
= > a = 7 or a = 1
Age can't be 1 years, it won't satisfy the situation.
Thus,
Present age of son is 7 years.
Present age of father is 49[ 7^2 ] years.
Let present age of son = x years.
According to question
Now, present age of father = x² years
One year ago :-
Age of father = 8 × Age of son
Present age - 1 year = 8x
x² - 1 = 8(x - 1)
x² - 1 = 8x - 8
x² - 8x + 8 - 1 = 0
x² - 8x + 7 = 0
x² - 7x - x+ 7 = 0
x(x - 7) - (x - 7) = 0
(x - 7)(x - 1) = 0
x = 7, 1
x = 1
neglected
So;
Present age of son = 7 years.
Present age of father = 49 years