Originally Posted by

**emakarov** It's 59.5% that is the percentage of water.

First, you can calculate the mass of H3PO4 in the original 1000kg slurry and thus find 1% of the phosphoric acid present in the initial slurry. This will be used later.

It is not clear from the problem text in what proportions the components of the solution are retained by the filtration. I mean, there is 2.5% w/w H2SO4 in the solution, but filtration theoretically may retain all H2SO4 and some water, but none of H3PO4. I don't think it is possible to calculate anything without this information.

Most likely, however, filtration preserves the ratio of the solution components. Since the solids account for 50% of the first cake, the cake's mass is 400kg, and the solution's mass is also 200kg. Using the proportions above, you can find the mass of each solution component.

After that let x kg of water has been added. Then the concentrations of the three components of the liquid solution in the new slurry can be expressed through x.

In the second cake, the same 200kg of solids constitute 55%, so you know the mass of the cake and the mass of its liquid part. Therefore, using the concentration of H3PO4 you found, you can calculate the mass of H3PO4 as an expression of x. Finally, it is equated to the 1% of the H3PO4in the initial slurry that you found in the beginning to form an equation for x.