Variance $=5$ and $n=20$
$\because \quad$ Variance $=5=\frac{1}{n} \Sigma(x i-\bar{x})^2$
$$
\Rightarrow \quad \Sigma(x i-\bar{x})^2=100...(1)
$$
Let after multiplication, the new observations be $y_1, y_2 \ldots y_{20}$ Where $y_i=2(x i)$ for some $i$...(2)
New variance $=\frac{1}{2} \Sigma\left(y_i-y\right)^2$ where $\bar{y}=\frac{1}{n} \Sigma y_i$
$$
\Rightarrow \bar{y}=\frac{1}{20} \Sigma 2 x i=2\left(\frac{1}{20} \Sigma x i\right)=2 \bar{x}...(3)
$$
$\because \quad \Sigma(x i-\bar{x})^2=100$
\{from (1)\}
$\Rightarrow \quad \Sigma\left(\frac{1}{2} y_i-\frac{1}{2} \bar{y}\right)^2=100$
$\Rightarrow\left(\frac{1}{2}\right)^2 \Sigma\left(y_i-y\right)^2=100 \Rightarrow \Sigma\left(y_i-y\right)^2=400$
$\therefore$ New variance $=\frac{1}{n} \Sigma(y i-\bar{y})^2=\frac{1}{20} \times 400=20$