$10($c$)$ A waste stream contains particles of three sizes: large, medium, and small. The large, medium and small particles account for $50\%,30\%$ and $20\%$ by weight in the gas stream, respectively. We pass this gas stream through a collector that is $99\%$ efficient on large particles, $75\%$ efficient on medium particles, and $30\%$ efficient on small particles, $($i$)$ what is the overall weight percent efficiency of this collector? $($ii$)$ If we add two more collectors, identical to the first collector, downstream of it$,$ what will the overall collection efficiency be$?$