$$\eqalign{ & {\text{Deflection max }}\left( {\text{A}} \right) = \frac{{{\text{P}}{{\text{L}}^3}}}{{48{\text{E}}I}} \cr & {\text{Deflection max }}\left( {\text{B}} \right) = \frac{{5{\text{w}}{{\text{L}}^4}}}{{384{\text{E}}I}};\,\,\,\left( {{\text{w}} = \frac{{\text{P}}}{{\text{L}}}} \right) \cr & = \frac{{5{\text{P}}{{\text{L}}^3}}}{{384{\text{E}}I}} \cr & {\text{Ratio}} = \frac{{{\text{P}}{{\text{L}}^3}}}{{48{\text{E}}I}} \times \frac{{384{\text{E}}I}}{{5{\text{P}}{{\text{L}}^3}}} = \frac{8}{5} \cr} $$

A three-hinged arch is a structural form used in civil engineering to efficiently distribute loads and resist bending moments. It consists of three hinges, which allow rotation at supports to accommodate arch's deformation under load. The three hinges are located at supports and at crown of arch.

The crown of an arch refers to highest point along arch's curve, where arch is subjected to compressive forces. Placing a hinge at crown allows arch to rotate and adapt to changes in loading and deformation. This rotational flexibility is crucial for arch's stability and ability to carry loads without excessive stress.

Note: Options A, C, and D are not accurate descriptions of typical hinge locations in a three-hinged arch. The correct configuration involves hinges at supports and at crown to ensure proper load distribution and structural performance.