An optically active compound A upon acid catalyzed hydrolysis yield two optically active compound B & C by first order kinetics.It is given that $[\alpha_0]$ for $A,B$ & C are $60^o,40^o$ & $-80^o$ respectively.If observed both of the mixture after 20 minute was $5^o$ while after completion of the reaction it was $-20^o$.What is $t_{1/2}$ of reaction?

Question

$\begin{array}{1 1}(a)\;10minutes&(b)\;5minutes\\(c)\;20minutes&(d)\;40minutes\end{array}$