A man is four times older than his son now. Eight years ago, the product of their ages was 220years.How old is the son now.
Answers
Answer:
13 year.
Step-by-step explanation:
Let the present age of son be a year. So present age father should be 4a year since it's for times of son's age.
Eight year ago:
Age of father = present age - 8
= 4a - 8 [ in year ]
Age of son = present age - 8
= a - 8 [ in year ]
Given,
Eight years ago, the product of their ages was 220.
⇒ ( 4a - 8 )( a - 8 ) = 220
⇒ 4a^2 - 32a - 8a + 64 = 220
⇒ 4a^2 - 40a + 64 = 220
⇒ a^2 - 10a + 16 = 55
⇒ a^2 - 10a + 16 - 55 = 0
⇒ a^2 - 10a - 39 = 0
⇒ a^2 - ( 13 - 3 )a - 39 = 0
⇒ a^2 - 13a + 3a - 39 = 0
⇒ a( a - 13 ) + 3( a - 13 ) = 0
⇒ ( a - 13 )( a + 3 ) = 0
⇒ a - 13 = 0 or a + 3 = 0
⇒ a = 13 or - 3 { age can't be negative so a = 13 }
Therefore present age of son is 13 year.
Step-by-step explanation:
Aloha !
Given that,
A man is four times older than his son.
Such that age of man= 4 a
Where 'a' is variable or integer
Age of son = a
Eight Ago:-
Age of man=4a-8
Age of son=a-8
Also given that, product of their ages was 220years. Such that,
(4a-8)(a-8)=220
4a²-32a-8a+64=220
4a²-40a+64=220
Taking 4 common
4(a²-10a+16)=220
a²-10a+16=220/4
a²-10a+16=55
a²-10a+16-55=0
a²-10a-39=0
a²-13a+3a-39=0
a(a-13) +3(a-13)=0
(a-13)(a+3)=0
a-13=0 and a+3=0
a=13 and a=-3
Negative value doesn't exist
Such that,
a=13
Therefore son's age is 13.
Father's age =4a-8
=4(13)-8
=52-13
=44