Example $12\mathrm{.}4$: A soil in the borrow pit is at a dry density of $17k\frac{N}{m^3}$ with a moisture content

of $10\%.$ The soil is excavated from this pit and compacted in a embankment to a dry density of

$18k\frac{N}{m^3}$ with a moisture content of $15\%.$ Compute the quantity of soil to be excavated from

the borrow pit and the amount of water to be added for $100m^3$ of compacted soil in the em$-$

bankment.