• # question_answer 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

$x+y=100$ $xy=\text{ }495\times 5=2475$ $\therefore$${{(x+y)}^{2}}-4xy={{(x-y)}^{2}}=1000$ $\left[ \because \,\,{{\left( x+y \right)}^{2}}-4xy={{\left( x-y \right)}^{2}} \right]$ ${{(x+y)}^{2}}-4xy=10000-9900$ ${{(x-y)}^{2}}=100$ $\therefore$    $x-y=10$