A soil sample has been compacted using a standard proctor test with $20\%$ moisture content. The Unit weight of the compacted soil sample is $20k\frac{N}{m^3}.$

What will be the saturated unit weight for this soil sample If we bring the soil sample to the fully saturated state $($i$.$e$.S=1)$ by adding water? The water unit weight and soil$-$specific gravity are $10k\frac{N}{m^3}$ and $2\mathrm{.}75,$ respectively.

Hint $1$: You will need first to calculate the void ratio $($e$)$ for the compacted soil $($you have the moisture content and unit weight and Gs is $2\mathrm{.}75),$ Then use the void ratio and Gs to calculate the saturated unit weight.

Hint $2$: You can use the following equation as part of your solution:

$\backslash$table$[[\frac{\text{S}\text{a}\text{t}\text{u}\text{r}\text{a}\text{t}\text{e}\text{d}\text{u}\text{n}\text{i}\text{t}\text{w}\text{e}\text{i}\text{g}\text{h}\text{t}({}_{\text{s}\text{a}\text{t}})}{\text{G}\text{i}\text{v}\text{e}\text{n}},],[G_s,e,\frac{(G_s+e){}_k}{1+e}$