Question

The sum of the ages of a father and son is 45 years. Five years ago ,the product is 124 find ages of their present ages

Answer 1

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

Given,

Sum of their ages = 45

Product of their ages five years ago = 124

Assume

Present age of father be p and son age be t

So,

p + t = 45 ..... (1)

$\textbf{\underline{Five\;years\;before\;their\;ages}}$  

Father = (p - 5)

Son = (t - 5)

Product of their ages = 124

(p - 5)(t - 5) = 124

(45 - t - 5)(t - 5) = 124  

40t - t² - 200 + 5t = 124  

t²  - 45t  + 324 = 0  

t²  - 36t  - 9t + 324 = 0

t(t - 36) - 9(t - 36) = 0

(t - 36)(t - 9) = 0

t = 9

or,

t = 36

${\boxed{\sf\:{Substitute\;value\;of\;t\;in\;(1) :-}}}$

p + t = 45

p + 9 = 45

p = 45 - 9

p = 36

$\huge{\boxed{\sf\:{Son\;is\;9\;years\;old\;and\;Father\:is\;36\;years\;old}}}$

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)

$\rule{300}{1.5}$

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

$\rule{300}{1.5}$

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.