Question

Sum of two numbers is $407$. The sum and difference of their LCM and HCF are $925$ and $851$ respectively. The difference of two numbers is

• A. $518$
• B. $185$
• C. $158$
• D. $175$

Answer 1

The correct option is B $185$

Let the two numbers: be $x$ & $y$

$\therefore x+y=407$ ......... $\left(1\right)$

Acc to the question,

$LCM+HCF=925$ .......... $\left(2\right)$

$LCM-HCF=851$ ......... $\left(3\right)$

On subtracting $\left(2\right)$ & $\left(3\right)$

$LCM+HCF=925-LCM+HCF=-851\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_2HCF=74HCF=37$

$\therefore LCM-\left(37\right)=857$

$LCM=857+37$

$=888$

As we know, $LCM\times HCF=$ product of two numbers

$\therefore 888\times 37=xxy$ ............. $\left(4\right)$

From $\left(1\right)$,

$x=(407-y)$

$\therefore 888\times 37=(407-y)y$

$\Rightarrow y^2-407y+832856$

$(y-111)(y-296)$

$\therefore x=296$ and $y=111$

$\therefore$ Difference of two numbers $=296-111$

$=185$

$\therefore$ Option $B$ is correct.