Question
If the sum of two numbers is 55 and the H.C.F. and L.C.M. of these numbers are 5 and 120 respectively, then the sum of the reciprocals of the numbers is equal to:
Answer: Option C
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Let the numbers be a and b.
Then, a + b = 55 and ab = 5 x 120 = 600.
Threrefore The required sum = \(\frac{1}{a}+\frac{1}{b}=\frac{a+b}{ab}=\frac{55}{600}=\frac{11}{120}\)
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