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 $1\mathrm{.}5kg$

$N{a}_2{S}_2{O}_3-5H_2\frac{O}{100}kg$ 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

$!$Kindly show the problem's full illustration or diagram!