$100$ kilograms per hour of quartz $($specific gravity $=2\mathrm{.}63)$ is being classified to three size fractions. A double$-$deck vibratory screen $(2$ screens of different mesh number$)$ is therefore used. The feed is being introduced at the upper deck screen. The middle fraction has a particle sizes ranging from $1\mathrm{.}175$ mm to $3\mathrm{.}3$ mm$.$ The middle fraction is being collected at a rate of $69\mathrm{.}40$ kilograms per hour while the proportion of the undersize of the lower deck screen to the middle fraction is $1$:$5\mathrm{.}5.$ Shown below is the laboratory result of the screen analysis of different streams:

Solve for the overall effectiveness of the screen and effectiveness of the lower deck.

$\backslash$table$[[$Mesh$,\backslash$table$[[$Coarse$],[($Oversize of$],[$upper deck$],[$screen$)]],$Middle,$\backslash$table$[[$Fines$],[($Undersize of$],[$lower deck$],[$screen$)]]],[\frac{3}{4},14\mathrm{.}00,1\mathrm{.}41,0\mathrm{.}86],[\frac{4}{6},50\mathrm{.}00,2\mathrm{.}50,0\mathrm{.}21],[\frac{6}{8},24\mathrm{.}00,33\mathrm{.}69,5\mathrm{.}33],[\frac{8}{10},8\mathrm{.}00,30\mathrm{.}80,27\mathrm{.}91],[\frac{10}{14},4\mathrm{.}00,20\mathrm{.}70,21\mathrm{.}73],[\frac{14}{20},,10\mathrm{.}20,19\mathrm{.}43],[\frac{20}{28},,0\mathrm{.}70,14\mathrm{.}81],[\frac{28}{35},,,9\mathrm{.}72]]$