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      Question

      Two numbers add up to 98. If the LCM of the numbers is 315

      and the HCF is 9, find the smaller of the two numbers.
      A 58 Correct Answer Incorrect Answer
      B 45 Correct Answer Incorrect Answer
      C 32 Correct Answer Incorrect Answer
      D 24 Correct Answer Incorrect Answer

      Solution

      ATQ,

      Let the smaller number = ‘x’

      Greater number = (98 – x)

      Product of the numbers = product of their LCM and HCF

      Or, x(98 – x) = 9 × 315

      Or, 98x – x² = 2835

      Or, x² – 98x + 2835 = 0

      Or, x² – 63x – 35x + 2835 = 0

      Or, x(x – 63) – 45(x – 63) = 0

      Or, (x – 63)(x – 45) = 0

      Or, x = 63, 45

      So, smaller number = 45

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