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    Question

    Sum of the two numbers is 49 and their HCF and LCM are 7

    and 70, respectively. Find the sum of reciprocal of the given two numbers.
    A (1/14) Correct Answer Incorrect Answer
    B (1/10) Correct Answer Incorrect Answer
    C (3/35) Correct Answer Incorrect Answer
    D (2/21) Correct Answer Incorrect Answer

    Solution

    Let the two numbers be '7a' and '7b', where 'a' and 'b' are co-prime numbers. 7a + 7b = 49 Or, 7 X (a + b) = 49 Or, a + b = (49/7) So, a + b = 7 We know that product of two numbers = HCF of the two numbers X LCM of the two numbers Or, 7a X 7b = 7 X 70 Or, ab = (7 X 70)/(7 X 7) = 10 therefore, sum of reciprocals = (a+b)/(7ab) = 7/70 = 1/10 Hence, option b.

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