A person uses a concave mirror for shaving. He places his face at a...

For a shaving mirror, the image formed is virtual, erect, and enlarged. Therefore, the magnification is positive.

Given $u = -25 \text{ cm}$ and $m = +1.4$.

Using the relation between magnification, focal length, and object distance:

$m = \dfrac{f}{f - u}$

Substituting the values:

$1.4 = \dfrac{f}{f - (-25)}$

$1.4(f + 25) = f$

$1.4f + 35 = f$

$0.4f = -35$

$f = -\dfrac{35}{0.4} = -87.5 \text{ cm}$

The focal length of the concave mirror is $87.5 \text{ cm}$.