Question

the sum of ages of a man and his son is 45. Five years ago,the product of their ages is 124. Find their present age??​

Answer 1

Answer:

• Ages of father and his son is 36 and 9 years.

Step-by-step explanation:

Given:

• Sum of ages of man and his son = 45
• Five years ago the product of their ages = 124

To Find:

• Present age of son and his son.

Let present age of son be 'x'.

And, present age of man be '45 - x'

Now, according to question,

Now, Five years ago,

=> (x - 5)(45 - x - 5) = 124

=> (x - 5)(40 - x) = 124

=> 40x - x² - 200 + 5x = 124

=> x² - 45x + 324 = 0

=> x² - 36x - 9x + 324 = 0

=> x(x - 36) - 9(x - 36) = 0

=> (x - 9)(x - 36) = 0

=> x = 9 and 36

So, son's age = 9 years because son is not older than father.

Father's age = 45 - 9 = 36 years.

Hence, Ages or father and his son is 36 and 9 years.

Answer 2

Answer:

Father is 36 years old and Son is 9 years old.

Step-by-step explanation:

Given :

Sum of their ages = 45

Product of their ages 5 years ago = 124

To find :

Thier present ages

Solution :

Let the present ages be -

• Son's age as y
• Father's age as x

⇒ x + y = 45 ..... (1)

Ages 5 years back -

• Son = (y - 5)
• Father = (x - 5)

Product of their ages = 124

⇒ (x - 5)(y - 5) = 124

⇒ (45 – y - 5) ×(y – 5) = 124  

⇒ 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 = 9 or y = 36

Put the value of y in Equation 1 -

⇒ x + y = 45

⇒ x + 9 = 45

⇒ x = 45 - 9

⇒ x = 36

Father's age = 36

$\therefore$ Father is 36 years old and Son is 9 years old.