If a man's face is $25cm$ in front of a concave shaving mirror producing an erect image $1.5$ times the size of the face, the focal length of the mirror would be

The correct option is A

$75cm$

Step 1: Given

Object distance, $u=-25cm$

Magnification, $m=1.5$

Step 2: Determine the image distance

Magnification is given by,

$$\begin{gathered} m=-\frac{v}{u} \\ 1.5=-\frac{v}{(-25)} \\ v=\frac{75}{2}cm \end{gathered}$$

Step 3: Determine the focal length

Using mirror formula,

$$\begin{gathered} \frac{1}{f}=\frac{1}{v}+\frac{1}{u} \\ =\frac{1}{{\displaystyle \frac{75}{2}}}+\frac{1}{(-25)} \\ =-\frac{1}{75} \\ \Rightarrow f=-75 \end{gathered}$$

(-ve sign implies that the focus is in front of the mirror)

Hence, option (A) is the correct option.