The LCM and HCF of two numbers are 495 and 5. If the sum of the numbers is 100, what is the difference of the numbers?

Question: The LCM and HCF of two numbers are 495 and 5. If the sum of the numbers is 100, what is the difference of the numbers?

Solution:
let,
one number is x
∴ another number is (100 - x)

∴ x(100 - x) = 5 × 495
or, 100x - x² = 2475
or, x² - 100x + 2475 = 0
or, x² - 55x - 45x + 2475 = 0
or, x(x - 55) - 45(x - 55) = 0
or, (x - 55)(x - 45) = 0
∴ x = 45, 55
∴ the numbers are 45 and 55.
difference = 55 - 45 = 10