Question

The LCM of two numbers is $495$ and their HCF is $5$. If the sum of the numbers is $100$ then their difference is:

• A. $10$
• B. $46$
• C. $70$
• D. $90$

Answer 1

The correct option is A $10$

Let one number $=x$ Then other number $=100-x$
LCM $=495$ and $HCF=5$
Product of number $=HCF\times LCM$
$\therefore x(100-x)=495\times 5$
$\Rightarrow 100x-x^2=2475$
$\Rightarrow x^2-100x+2475=0$
$\Rightarrow x^2-45x-55x+2475=0$
$\Rightarrow x(x-45)-55(x-45)=0$
$\Rightarrow (x-45)(x-55)=0$
$\Rightarrow x=45$ or $55$
$\therefore$ The one numbers is $45$, then another number $=100-45=55$ or

if one number is $55,$ then another number $=100-55=45$
$\therefore$ Required difference $=55-45=10$