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

A. 10

B. 40

C. 70

D. 90

Answer: Option A

Solution(By Examveda Team)

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 x = 45
∴ The numbers are 45 and 55
Required difference = (55 - 45) = 10