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Given: The L.C.M. of two numbers is 495 and their HCF is 5. The sum of the two numbers is 100 Formula used: Product of the two number = LCM × HCF Calculation: Let the one number be x and another number be 100 - x According to the question, ⇒ x(100 - x) = 495 × 5 ⇒ 100x - x2 = 2475 ⇒ x2 - 100x + 2475 = 0 ⇒ x2 - 55x - 45x + 2475 = 0 ⇒ x(x - 55) - 45(x - 55) = 0 ⇒ (x - 55)(x - 45) = 0 ⇒ x = 55 or 45 If one number is 45 then another number 100 - 45 = 55 Or one number is 55 then another number 100 - 55 = 45 Their difference is 55 - 45 = 10 ∴ Their difference is 10. India’s #1 Learning Platform Start Complete Exam Preparation
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