Question

Choose the correct answers from the alternatives given.
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 $10$

$\Rightarrow$ Let the numbers be $x$ and $(100-x)$

According o the question,

$\Rightarrow$ $x(100-x)=5\times 495$

$\Rightarrow$ $100x-x^2=2475$

$\Rightarrow$ $x^2-100x+2475=0$

$\Rightarrow$ $x^2-55x-45x+2475=0$

$\Rightarrow$ $x(x-55x)-45(x-55)=0$

$\Rightarrow$ $(x-55)(x-45)=0$

$\Rightarrow$ $x-55=0$ and $x-45=0$

$\therefore$ $x=55$ and $x=45$

$\therefore$ The numbers are $45$ and $55$

$\Rightarrow$ Required difference $=55-45=10$