The L.C.M of two numbers is 495 and their H.C.F is 5. If the sum of the numbers is 100, then their difference is

Let the numbers be x and (100-x).

Then, $x100-x=5*495$

 =>   $x2-100x+2475=0$

 =>  (x-55) (x-45) = 0

 =>  x = 55 or x = 45

  The numbers are 45 and 55

Required difference = (55-45) = 10