To determine the relationship between the maximum bending stresses induced in beams (A) and (B), we can analyze the bending moment equations and the concept of the section modulus.

1. Bending Moment Equations:
The bending moment equations for beams (A) and (B) can be derived from the basic beam bending theory. Assuming a simply supported beam with a concentrated load at the center, the bending moment equation can be expressed as:

For beam (A):
M(A) = (w * L^2) / 8

For beam (B):
M(B) = (w * L^2) / 16

where M(A) and M(B) are the bending moments applied to beams (A) and (B) respectively, w is the load per unit length, and L is the span length.

2. Section Modulus:
The section modulus is a geometric property of a beam cross-section that relates to its ability to resist bending moments. It is defined as the moment of inertia divided by the maximum distance from the centroid to the outermost fibers of the cross-section.

For beam (A):
Section modulus (Z(A)) = (b * (d/2)^2) / 6 = (b * d^2) / 24

For beam (B):
Section modulus (Z(B)) = (b^2 * d^2) / 6

3. Relationship between Maximum Bending Stresses:
The maximum bending stress (σ) in a beam can be calculated using the bending moment equation and the section modulus:

For beam (A):
σ(A) = M(A) / Z(A) = [(w * L^2) / 8] / [(b * d^2) / 24] = (3wL^2) / (2bd^2)

For beam (B):
σ(B) = M(B) / Z(B) = [(w * L^2) / 16] / [(b^2 * d^2) / 6] = (3wL^2) / (8b^2d^2)

4. Comparing the Maximum Bending Stresses:
By comparing the expressions for σ(A) and σ(B), we can observe the following relationship:

σ(A) / σ(B) = [(3wL^2) / (2bd^2)] / [(3wL^2) / (8b^2d^2)] = (8b^2d^2) / (2bd^2) = 4b

Therefore, the maximum bending stresses induced in beams (A) and (B) are related as 4b, or option (d) in the given choices.

In conclusion, when the bending moments applied to beams (A) and (B) are the same, the maximum bending stresses induced in these beams are related to each other as 4b, where b is the width of beam (A).