SSC JE Civil Engineering 23-Mar-2021 Shift 1 Paper

Concept:
While excavating the soil from the borrow pit and after that compacting it, the mass of solids and its specific gravity will not change, and hence, the volume of solids remains constant even after compaction.
The Total volume(V) of soil is given by
$\mathrm{V}={\mathrm{V}}_{\mathrm{v}}+{\mathrm{V}}_{\mathrm{s}}$
Where $\mathrm{V}=$ Total volume of soil, ${\mathrm{V}}_{\mathrm{V}}=$ Volume of voids, ${\mathrm{V}}_{\mathrm{s}}=$ Volume of solids
Divide the equation (i) by ${\mathrm{V}}_{\mathrm{s}}$ (Volume of solids)
$\frac{\mathrm{V}}{{\mathrm{V}}_{\mathit{s}}}=\frac{{\mathrm{V}}_{\mathrm{v}}}{{\mathrm{V}}_{\mathrm{s}}}+\frac{{\mathrm{V}}_{\mathrm{s}}}{{\mathrm{V}}_{\mathrm{s}}}$
  $\frac{\mathrm{V}}{{\mathrm{V}}_{\mathrm{z}}}=\frac{{\mathrm{V}}_{\mathrm{v}}}{{\mathrm{V}}_{\mathrm{s}}}+1$
$\frac{\mathrm{V}}{{\mathrm{V}}_{\mathit{s}}}=\mathrm{e}+1$
${\mathrm{V}}_{\mathrm{S}}=\frac{\mathrm{V}}{\left(1+\mathrm{e}\right)}$
Calculation:
Condition - I: Filling
${\mathrm{e}}_{\mathrm{f}}=0.7$ and ${\mathrm{V}}_{\mathrm{f}}=8,50,000{\mathrm{m}}^3$
So, Volume of solids in filling $\left({\mathrm{V}}_{\mathrm{sf}}\right)$
${\mathrm{V}}_{\mathrm{sf}}=\frac{{\mathrm{V}}_{\mathrm{f}}}{\left(1+{\mathrm{e}}_{\mathrm{f}}\right)}=\frac{850000}{\left(1+0.7\right)}=500000{\mathrm{m}}^3$
Condition-I: Excavation
The volume of solids will be the same as that of during fill i.e. ${\mathrm{V}}_{\mathrm{sf}}=500000{\mathrm{m}}^3$
${\mathrm{e}}_{\mathrm{e}\mathrm{x}\mathrm{c}}=0.8$
So, find the volume of excavated soil $\left({\mathrm{V}}_{\mathrm{exc}}\right)$
${\mathrm{V}}_{\mathrm{s}\left(\mathrm{exc}\right)}=\frac{{\mathrm{V}}_{\mathrm{exc}}}{\left(1+{\mathrm{e}}_{\mathrm{exc}}\right)}$
$500000=\frac{{\mathrm{V}}_{\mathrm{exc}}}{\left(1+0.8\right)}$
${\mathrm{V}}_{\mathrm{exc}}=500000\times \left(1+0.8\right)=900000{\mathrm{m}}^3$
The estimated cost for the filling work is (in Rs.) = 10 × 900000 = 90,00,000