$($b$)$ Fresh orange juice containing $14\%$ solids and the balance water is fed to an evaporation process at a rate of $650kgh{r}^{-1}.$ It is concentrated to $61\%$ solids and this concentrate is combined with fresh juice that bypasses the process to give a final product having $42\%$ solids. Assuming no loss of juice solids to water, draw a flow diagram of the process and determine:

$($i$)$ the rate at which orange juice concentrate $(42\%$ solids$)$ is produced;

$($ii$)$ the fraction of the product that comes from the bypass stream

$($iii$)$ the flow rates of the bypass and "evaporator concentrate" streams.