Final answer:
A genuine picture formed by a concave mirror is four times taller than the object positioned 10 cm in front of it. The image is 40 centimeters behind the mirror.
Step-by-step explanation:
When a concave mirror forms a real image, the object is placed beyond the focal point. In this case, the concave mirror forms a real image that is four times as tall as the object. This means that the height of the image is four times the height of the object. Since the image is real and upright, the position of the image must be in front of the mirror.
Using the mirror formula:
1/f = 1/v - 1/u
We can substitute the given values:
v = 4u
Simplifying the equation:
1/f = 1/4u - 1/u
1/f = -3/4u
4u = -3fu
4 = -3f
f = -4/3
The negative sign indicates that the image is formed behind the mirror. So, the position of the image is 40 cm behind the mirror (B).