(a) 10.
Let one number = x. Then,
Other number = 100 – x
LCM = 495, HCF = 5
⇒ x(100 – x) = 495 × 5
⇒ 100x – x2 = 2475
⇒ x2 – 100x + 2475 = 0
⇒ x2 – 45x – 55x + 2475 = 0
⇒ x (x – 45) – 55(x – 45) = 0
⇒ (x – 45) (x – 55) = 0
⇒ x = 45 or 55.
∴ The numbers and 45, 100 – 45 = 55 or 55, 100 – 55 = 45
Required difference = 55 – 45 = 10.