A finely divided solids feed, of $150k\frac{g}{h},$ containing $\frac{1}{3}$ water$-$ soluble $N{a}_{2}C{O}_3$ and $\frac{2}{3}$

insoluble ash is to be leached and washed at $30C$ in a countercurrent system with $400k\frac{g}{h}$

of water. Experiments show that the sludge underflow will contain $2kg$ of liquid $($water

and carbonate$)$ per kg of insoluble ash. Assuming ideal stages, calculate the flowrates and

compositions of the overflow and underflow.