Answer
See the detailed answer below.
Work Step by Step
$$\color{blue}{\bf [a]}$$
We know that the magnification of a telescope is given by
$$M= \dfrac{\theta_{\rm eye}}{\theta_{\rm object}}=-\dfrac{f_{\rm object}}{f_{\rm eye}}$$
$$M= -\dfrac{f_{\rm object}}{f_{\rm eye}}\tag 1$$
we are given that $f_{\rm object}=1.0\;\rm m=100\;cm$, so we need to find $f_{\rm eye}$; where we know that the angular magnification of a magnifying glass is given by
$$M_{\rm eye}=\dfrac{25\;\rm cm}{f_{\rm eye}}$$
Hence,
$$f_{\rm eye}=\dfrac{25\;\rm cm}{M_{\rm eye}}=\dfrac{25}{10}=\bf 2.5\;\rm cm$$
Plugging into (1);
$$M= -\dfrac{f_{\rm object}}{f_{\rm eye}} =-\dfrac{100}{2.5}=\color{red}{\bf -40}$$
$$\color{blue}{\bf [b]}$$
We know that the $f_{\rm number}$ is given by
$$f_{\rm number}=\dfrac{f}{D}$$
Plugging the known;
$$f_{\rm number}=\dfrac{100}{20}=\color{red}{\bf 5}$$
