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:

A \(\frac{601}{55}\)

B \(\frac{129}{25}\)

C \(\frac{11}{120}\)

D \(\frac{55}{601}\)

Correct Answer: Option C

Let the numbers be a and b.

Then, a + b = 55 and ab = 5 x 120 = 600.

The required sum = \(\frac1a+\frac1b\) = \(\frac{a+b}{ab}\) = \(\frac{55}{600}\) = \(\frac{11}{120}\)