Reciprocal of numbers

let $x$ and $y$ be the numbers, then

$\dfrac{1}{x}+\dfrac{1}{y}=11$ $\large \implies$ $\dfrac{1}{y}=11-\dfrac{1}{x}$ $\color{#D61F06}(1)$

and

$3 \left(\dfrac{1}{x} \right)=3+2 \left(\dfrac{1}{y} \right)$ $\color{#D61F06}(2)$

Substitute $\color{#D61F06}(1)$ in $\color{#D61F06}(2)$ , we have

$3 \left(\dfrac{1}{x} \right)=3+2 \left(11-\dfrac{1}{x} \right)$

$\dfrac{3}{x}=3+22-\dfrac{2}{x}$

$\dfrac{3}{x}+\dfrac{2}{x}=25$

$\dfrac{5}{x}=25$

$x=\dfrac{5}{25}=\dfrac{1}{5}=$ $\boxed{0.2}$