Question $2$

An ore contains Pyrolusite $($:$(Mn{O}_2)SG-4\mathrm{.}79\}$ and Silica $(Si{O}_2)(SG-2\mathrm{.}65)$

The feed grade to a two stage DMS plant is $25\%Mn.$

The feed rate is $200\frac{V}{h}r.$

The bath density in the first stage is $2\mathrm{.}85$ and $75\%$ of the Silica in the feed is rejected in the float product.

The sink product is then recrushed to $-50mm$ and screened at $5mm.$

The $-5mm$ fraction mass is $10\%$ of the first stage sinks mass and contains $10\%Mn.$

The $-50+5mm$ is then retreated in a second stage DMS circuit and $85\%$ of the contained Pyrolusite is recovered in the sinks at an SQ of $4\mathrm{.}53.$