The HCF and the LCM of two numbers are 5 and 120, respectively. If the sum of the two numbers is 55, then the sum of the reciprocals of these two numbers is equal to:

$\frac{11}{120}$

Let the numbers be a and b.

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

The required sum = \(\frac{1}{a}\) + \(\frac{1}{b}\)  = \(\frac{a + b}{ab}\)  = \(\frac{55}{600}\)  = \(\frac{11}{120}\)