The LCM of two numbers is 495 and their HCF is 5. If the sum of the nu

1.	The LCM of two numbers is 495 and their HCF is 5. If the sum of the numbers is 100, then their difference is (a) 10 (b) 46 (c) 70 (d) 90
Answer» (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.

The LCM of two numbers is 495 and their HCF is 5. If the sum of the numbers is 100, then their difference is (a) 10 (b) 46 (c) 70 (d) 90

Answer»

(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.