Question

A man is five times as old as his son and the sum of the squares of their ages is $2106$. Find their ages.

• A. $9$ years & $45$ years
• B. $10$ yrs & $50$ years
• C. $12$ years & $48$ years
• D. $16$ years & $45$ years

Answer 1

Answer: (A)

$9$ years & $45$ years

Let the age of the son be $x$
$\therefore$ The age of his father $=5x$
Given that
${\left(5x\right)}^2+{\left(x\right)}^2=2106$
$25x^2+x^2=2106$
$x^2=\frac{2106}{26}=81$
$\therefore x=9$
$\therefore$ Age of son $=9$ years
Age of father $=5x9=45$ years