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      Question

      Sum of the two numbers is 81 and their HCF and LCM are 9

      and 180, respectively. Find the sum of reciprocal of the given two numbers.
      A (1/18) Correct Answer Incorrect Answer
      B (1/15) Correct Answer Incorrect Answer
      C (1/20) Correct Answer Incorrect Answer
      D (7/18) Correct Answer Incorrect Answer

      Solution

      Let the two numbers be '9a' and '9b', where 'a' and 'b' are co-prime numbers. 9a + 9b = 81 Or, 9 X (a + b) = 81 Or, a + b = (81/9) So, a + b = 9 We know that product of two numbers = HCF of the two numbers X LCM of the two numbers Or, 9a X 9b = 9 X 180 Or, ab = (9 X 180)/(9 X 9) = 20 therefore, sum of reciprocals = (a+b)/(9ab) = 9/180 = 1/20 Hence, option c.

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