Q$1$D

In a Marshall Design procedure for an asphalt mixture, the weight of aggregate $(W_s)$ is $1200\mathrm{.}0g,$ and the weight of asphalt binder $(W_b)$ is $76\mathrm{.}0g.$ The voids filled with asphalt $($VFA$)$ value is determined to be $73\mathrm{.}0\%,$ and the effective asphalt content by total weight of mixture $(P_{be})$ is found to be $3\mathrm{.}80\%.$ If the bulk specific gravity of aggregate $(G_{sb})$ is $2\mathrm{.}568,$ the specific gravity of asphalt binder $(G_b)=1\mathrm{.}030,$ and the density of water $({}_w)=1\mathrm{.}000\frac{g}{c}{m}^3,$ determine the following properties of the asphalt mixture:

a$.$ The absorbed asphalt binder content $(P_{ba}),$ percent by weight of aggregate

b$.$ The effective specifc gravity of the aggregate $(G_{se})$

c$.$ The bulk specifc gravity of the compacted asphalt mixture $(G_{mb})$

d$.$ The voids in mineral aggregate $($VMA$),$ percent by total volume of mixture

e$.$ The voids in total mixture $($VTM$),$ percent by total volume of mixture

f$.$ The theoretical maximum specifo gravity of the loose mixture $(G_{mm})$