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. $$\frac{{55}}{{601}}$$

B. $$\frac{{601}}{{55}}$$

C. $$\frac{{11}}{{120}}$$

D. $$\frac{{120}}{{11}}$$

Answer: Option C

Solution(By Examveda Team)

$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{numbers}}\,{\text{be}}\,a\,{\text{and}}\,b \cr & {\text{Then}},\,a + b = 55\,{\text{and}} \cr & ab = 5 \times 120 = 600 \cr & \therefore {\text{The}}\,{\text{required}}\,{\text{sum}} \cr & = \frac{1}{a} + \frac{1}{b} = \frac{{a + b}}{{ab}} = \frac{{55}}{{600}} = \frac{{11}}{{120}} \cr} $$