Analysis:

When a beam is subjected to a load, it deflects or bends. The magnitude of deflection depends on various factors such as the type of load, beam material, geometry, and support conditions. In this case, we have two equal length beams with fixed ends. One beam carries a distributed load, and the other carries the same load concentrated in the middle.

Comparison of Deflections:

To compare the deflections of the two beams, let's assume the distributed load on the first beam is w per unit length, and the concentrated load on the second beam is P. The length of both beams is denoted by L.

First Beam:
- Length of beam (L)
- Distributed load (w per unit length)
- Fixed-fixed support conditions

Second Beam:
- Length of beam (L)
- Concentrated load (P at the middle)
- Fixed-fixed support conditions

Deflection Calculation:

The maximum deflection for a beam with fixed-fixed support conditions carrying a distributed load occurs at the midpoint. The deflection at the midpoint of the first beam can be determined using the following formula:

δ = (5wL^4) / (384EI)

Where:
- δ is the deflection at the midpoint
- w is the distributed load per unit length
- L is the length of the beam
- E is the Young's modulus of the beam material
- I is the moment of inertia of the beam cross-section

For the second beam, since the load is concentrated at the midpoint, the deflection at the midpoint can be determined using the following formula:

δ = (PL^3) / (48EI)

Comparison of Maximum Deflections:

To compare the maximum deflections of the two beams, we can calculate their ratio:

Ratio = (deflection of the second beam) / (deflection of the first beam)

Substituting the values from the formulas above:

Ratio = [(PL^3) / (48EI)] / [(5wL^4) / (384EI)]

Ratio = (P / w) * (384 / 48) * (L^3 / L^4)

Ratio = (P / w) * 8 * (1 / L)

Since the beams are equal in length (L) and the loads are equal (P = wL), the ratio simplifies to:

Ratio = (P / w) * 8 * (1 / L)

Ratio = 8

Therefore, the ratio of the maximum deflections of the two beams is 8, which corresponds to option A.