It is given that sum of two numbers is 100. Let the two numbers be x and 100 – x and HCF is 5 and LCM is 495
=> We need to apply the formula: HCF × LCM = Product of two numbers
Which gives x(100 – x) = 495 × 5
Solving the equation we get a quadratic which looks like this:
x2 – 100x + 2475 = 0
=> (x – 55)(x- 45) = 0
Therefore, Two numbers are 55 and 45