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  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 :
    1. 10
    2. 46
    3. 70
    4. 90
Correct Option: A

Suppose 1st number is p then, 2nd number = 100 – p
As we know that ,
∴ LCM × HCF = 1st number × 2nd number
⇒ 495 × 5 = p × (100 – p)
⇒ 495 × 5 = 100p – p2
⇒ p2 – 55p – 45p – 2475 = 0
⇒ (p – 45) (p – 55) = 0
⇒ p = 45 or p = 55
Then, difference = 55 – 45 = 10



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