Multiple choice

\text{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
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A Correct answer
Explanation

Let numbers be a and b. Product = LCM × HCF = 495 × 5 = 2475. Also a + b = 100 and ab = 2475. Solving: a and b are roots of x² - 100x + 2475 = 0. The discriminant is 100² - 4(2475) = 10000 - 9900 = 100. Roots are (100 ± 10)/2 = 55 and 45. Difference = 55 - 45 = 10.

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