A rice grader receives feed containing18% broken kernels. The head-rice stream contains 3% brokens, and the broken stream contains 4% head rice. Find separation effectiveness based on head-rice separation, to three decimals.
Take unit feed with head fraction.82. Let product head-stream mass be P. Head balance gives $.82=.97P+.04(1-P)$,so $P=.78/.93=.8387097$. Recovery of head rice is $.97P/.82=.9921322$; recovery of broken rice to reject is $.96(1-P)/.18=.8602151$. Separation effectiveness is their product,$.8534470$,rounded **0.853**.