Titanium dioxide, the most common white pigment in paint, can be produced from the titanium mineral rutile by chlorination to TiCl4, followed by oxidation to TiO2. To purify insoluble TiO2, it is washed free of soluble impurities in a continuous, countercurrent system of thickeners with water. Two hundred thousand kg/h of 99.9wt%TiO2 pigment is to be produced by washing, followed by filtering and drying. The feed contains 50wt%TiO2,20wt% soluble salts, and 30wt% water. Wash liquid is pure water at a flow rate equal to the feed on a mass-flow basis. (a) Determine the number of washing stages required if the underflow from each stage is 0.4kg solution /kgTiO2. (b) Determine the number of washing stages required if the underflow varies as follows