$($c$)1,000\mathrm{.}00kg{h}^{-1}$ of a mixture of benzene $($B$)$ and toluene $($T$)$ containing

$50\%$ benzene by mass is separated by distillation into two fractions. The

mass flow rate of benzene in the top stream is $450\mathrm{.}00kgB{h}^{-1}$ and that of

toluene in the bottom stream is $475\mathrm{.}00kgT{h}^{-1}.$ The operation is at steady

state. What are the total flow rates of the top and bottom streams? What is

the toluene concentration $(w$ t $\%)$ in the top and bottom streams?

$($d$)$ The above distillation column was in operation for some time. The total

flows to the top and bottom streams were measured and found to be

$470\mathrm{.}25kg{h}^{-1}$ and $519\mathrm{.}75kg{h}^{-1},$ respectively. Are there losses in the

system and if so$,$ outline how these losses could be minimized.