Question

If the sum of two numbers is $55$ and H.C.F. and L.C.M. of these numbers are $5$ and $120$ respectively, then what is the sum of the reciprocals of these numbers?

• A. $\frac{55}{601}$
• B. $\frac{601}{55}$
• C. $\frac{11}{120}$
• D. $\frac{120}{11}$

Answer 1

The correct option is C $\frac{11}{120}$

Let the numbers be $a$ and $b$
Given $a+b=55$ and $a\times b=5\times 120=600$
Required sum $=\frac{1}{a}+\frac{1}{b}=\frac{a+b}{ab}$
$=\frac{55}{600}=\frac{11}{120}$