Grinding, classification and concentration circuit is given in the below figure. A hydrocyclone is fed at a rate of $20\frac{t}{h}$ of dry solids. The cyclone feed contains $30\%$ solids, the underflow $50\%$ solids, and the overflow $15\%$ solids by weight. The ball mill is operating with $55\%$ solids. Copper assays are given on the flowsheet for the concentration stage. According to the given data;

a$-$ Calculate the solids flowrate $)$ of underflow and overflow of the hydrocyclone.

b$-$ Determine the solids flowrate $)$ of new feed.

c$-$ Calculate the water flowrate $(\frac{t}{h})$ in the underflow stream.

d$-$ Determine the water amount $)$ which is added to the ball mill feed to operate the mill at $55\%$ solids.

e$-$ Calculate the recovery of the concentration process.