Question

the sum of the age of a father and his son is 45 years five years ago the product of their age was 4 times the father's age at the that time find their present age

Answer 1

ANSWER:-

HAPPY FRIENDSHIP DAY TO ALL MY FRIENDS.
Solution:-
Let the present age of father = x yrs and the present age of son = y yrs

According to question:

x + y = 45 ...(1)

Again, 5 years ago, the product of their ages was 124, therefore,

(Age of man 5 years ago) × (Age of son 5 years ago) = 124

(x – 5) × (y – 5) = 124

⇒ (45 – y - 5) ×(y – 5) = 124 [Using (1)]

⇒ 40y – y2 - 200 + 5y = 124

⇒ y2 - 45y + 324 = 0

⇒ y2 - 36y - 9y + 324 = 0

⇒ y(y - 36) -9 (y - 36) = 0

⇒ (y - 36)(y - 9) = 0

⇒ y = 36 or y = 9

For y = 36, x = 45 - 36 = 9 which is not possible.

For y = 9, x = 45 - 9 = 36

Therefore, the present age of father = 36 years and the present age of son = 9 years.

Answer 2

$\mathbf{Let \: present \: age \: of \: son \: is \: \: x \: years \: and \: present \: age \: of f ather \: is \: \: ( 45 - x ) \: years, }$



$\bold{Five \: years \: ago, } \\ \bold{ Age \: of \: son = ( x - 5 ) \: years } \\ \bold{Age \: of \: father= ( 45 - x - 5 ) \: years = ( 40 - x ) \: years }$



According to the question,


Product of age of son and father = 4 × father's age


=> ( 40 - x ) ( x - 5 ) = 4 ( 40 - x )

=> x - 5 = 4

=> x =4 + 5

=> x = 9





$\bold{Present \: age \: of \: son = x = 9 \: years} \\ \bold{ Present \: age \: of \: father = \: ( 45 - x ) = ( 45 - 9 ) = 36 \: years}$