Question

Ten years ago father was $12$ times as old as his son at that time and $10$ years hence he will be twice as old as his son. Find their present ages.

• A. $55$ years, $24$ years
• B. $34$ years, $12$ years
• C. $48$ years, $19$ years
• D. $42$ years, $18$ years

Answer 1

The correct option is B $34$ years, $12$ years

Ten years ago father was $12$ times as old as his son at that time
Let the age of the son before $10$ years $=x$ and age of the father before $10$ years $=12x$
$10$ years hence he will be twice as old as his son.

$2(x+10+10)=(12x+10+10)$
$\Rightarrow 2x+40=12x+20$

$\Rightarrow 10x=20$
$\Rightarrow x=2$
$\Rightarrow$ age of son at present$=x+10=2+10=12$
Age of the father at present$=12x+10=122+10=34$