The LCM of two numbers is 495 and their HCF is 5. If the sum of the numbers is 100, then their difference is = ?

Explanation:-

LCM = 495
HCF = 5       ( given )
∴ Let numbers are = 5x and 5y
∴ LCM = 5xy
⇒ 5xy = 495
⇒ xy = 99
∴ Possible co-prime factors are
1,       99
9,       11
∴ Possible numbers are 5x, 5y
45,       55
5,       495
Now given that sum of numbers = 100
So, required numbers are = (45, 55)
∴ Difference of numbers = 55 - 45 = 10