Problem$2$

An industrial $1000$kg water$-$oil mixture that is $20$ wt$\%$ oil, is treated in a two$-$stage process to separate

the oil from water. The first stage consisting of decantation results in a $100$kg mixture that is $75$ wt$\%$ oil.

The remaining part is treated through a separator, but for technical restrictions had to be further diluted

by adding $100$kg of water before feeding it into the separator. The output streams from the separator

consist of an oil$-$dilute $(5$ wt$\%)$ and an oil$-$concentrated $(90$ wt$\%)$ solution.

Determine:

$($a$)$ the oil mass concentration in the feed entering the separator,

$($b$)$ the masses of oil in the two output streams.