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:
$ \dfrac{55}{601} $
$ \dfrac{601}{55} $
$ \dfrac{11}{120} $
$ \dfrac{120}{11} $
Explanation:
Let the numbers be $ a $ and $ b $.
Then, $ a $ + $ b $ = 55 and ab = 5 x 120 = 600.
$\therefore$ The required sum =$ \dfrac{1}{a} $+$ \dfrac{1}{b} $=$ \dfrac{a + b}{ab} $=$ \dfrac{55}{600} $=$ \dfrac{11}{120} $