Question
Sum of the two numbers is 42 and their HCF and LCM are 6
and 72, respectively. Find the sum of reciprocal of the given two numbers.Solution
Let the two numbers be '6a' and '6b', where 'a' and 'b' are co-prime numbers. 6a + 6b = 42 Or, 6 X (a + b) = 42 Or, a + b = (42/6) So, a + b = 7 We know that product of two numbers = HCF of the two numbers X LCM of the two numbers Or, 6a X 6b = 6 X 72 Or, ab = (6 X 72)/(6 X 6) = 12 therefore, sum of reciprocals = (a+b)/(6ab) = 7/72 Hence, option c.
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