Question

If the sum of two numbers is $55$ and the $\text{H.C.F.}$ and $\text{L.C.M.}$ of these numbers are $5$ and $120$ respectively, then the sum of the reciprocals of the numbers is equal to

• A. $\frac{1}{12}$
• B. $\frac{11}{120}$
• C. $\frac{11}{55}$
• D. $\frac{1}{120}$

Answer 1

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

Let the two numbers be $a$ and $b.$
Then, $a+b=55$
We know $\text{H.C.F.}\times \text{L.C.M.}=ab$
$\Rightarrow ab=5\times 120=600$
$\therefore$ Required sum $=\frac{1}{a}+\frac{1}{b}=\frac{a+b}{ab}$
$=\frac{55}{600}=\frac{11}{120}$