The L.C.M of two numbers is 495 and their H.C.F is 5. If the sum of the numbers is 10, then their difference is__________?

A. 10
B. 46
C. 70
D. 90

Explanation:

Let the numbers be x and (100 – x).

Then, x(100 – x) = 5 * 495
x2 – 100x + 2475 = 0
(x – 55)(x – 45) = 0
x = 55 or 45
The numbers are 45 and 55.
Required difference = 55 – 45 = 10.