Question
Sum of the two numbers is 32 and their HCF and LCM are 4
and 60, respectively. Find the sum of reciprocal of the given two numbers.Solution
Let the two numbers be '4a' and '4b', where 'a' and 'b' are co-prime numbers. 4a + 4b = 32 Or, 4 X (a + b) = 32 Or, a + b = (32/4) So, a + b = 8 We know that product of two numbers = HCF of the two numbers X LCM of the two numbers Or, 4a X 4b = 4 X 60 Or, ab = (4 X 60)/(4 X 4) = 15 therefore, sum of reciprocals = (a+b)/(4ab) = 8/60 = 2/15 Hence, option a.
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