Question

The sum of ages of a father and his son is 45 years.5 years ago, the product of their ages was 124.determine their present age?

Answer 1

Let present age of father be f and son be s.

f+s=45 years; (f-5)(s-5)=124;

(f-5)(45-f-5)=124 [since s=45-f}

or,(f-5)(40-f)=124

or,40f-f^2+5f-200=124

or,45f-f^2 -324 =0

or, f^2 -45f +324=0

or,f^2 -36f-9f + (36x9)=0

or, f(f-36) -9(f-36)=0

or, (f-36)(f-9)=0

so. either f=36 and s=45-f=9

or,f=9 and s=45-f=36.

but f>s, so f=36 years and s=9 years.

Answer 2

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

Assumption

$\textbf{\underline{Present\;age\;of\;Father}}$

= p years p

$\textbf{\underline{Present\;age\;of\;Son}}$

= c years

$\textbf{\underline{Situation}}$

p + c = 45 ...(1)

$\textbf{\underline{Five\;years\;ago}}$

(p - 5) × (c - 5) = 124

(45 - c - 5) × (c - 5) = 124

40c - c² - 200 + 5y = 124

c² - 45c + 324 = 0

c² - 36c - 9c + 324 = 0

c(c - 36) - 9 (c - 36) = 0

(c - 36) (c - 9) = 0

(c - 36) = 0

c = 36

(c - 9) = 0

c = 9

$\textbf{\underline{Substitute\;the\;value\;in\;(1)}}$

p + c = 45

p + 9 = 45

p = 45 - 9

p = 36

$\textbf{\underline{Present\;age\;of\;Father}}$

= 36 years

$\textbf{\underline{Present\;age\;of\;Son}}$

= 9 years.