A binary A$-$B system shows eutectic reaction at $500$C and the equilibrium melting point of pure A is $800$C$.$ Both solidus and liquidus on the A$-$rich side are linear with partition coef cient of $0\mathrm{.}5.$ A rich solid solution is labelled as$.$ The maximum solubility of B in$$is $20$ wt$\%.$ If an alloy of bulk composition $10$wt$\%$ B is solidifying with equilibrium solidi cation conditions, what should be the solid fraction present at a temperature of $700$C$?$