An aqueous solution containing $60\%N{a}_2{S}_2{O}_3$ and $1\%$ soluble impurities is diluted with water and fed to a crystallizer where it is cooled in order to crystallize $N{a}_2{S}_2{O}_3-5H_{2}O.$ The crystals carry $0\mathrm{.}05kg$ of solution $($excluding impurities$)$ per kg of crystals. The free water present in the adhering solution is removed on drying the crystals. The final dried product contains not more than $0\mathrm{.}1\%$ impurity. The solubility of the hydrate is $1\mathrm{.}5kgN{a}_2{S}_2{O}_3-5H_2\frac{O}{100}kg$ free water. On the basis of $100kg$ of $60\%$ solution, calculate the following:

a$)$ the amount of water in kilograms before cooling

b$)$ the amount of crystals formed

c$)$ the percentage recovery of $N{a}_2{S}_2{O}_3$ in the dried hydrated crystals

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