In $2017,$ Ms$.$ Chiu invested in the common shares of three CCPCs $$ Corp A$,$ Corp B$,$ and Corp C$.$ She purchased $100$ Class A common shares of each corporation. She paid $$40,000$ for the shares of Corp A$,$ $$20,000$ for the shares of Corp B$,$ and $$80,000$ for the shares of Corp C$.$

Before her investment, each corporation had $400$ Class A common shares. The total amount invested in the Class A shares, prior to Ms$.$ Chiu$$s investment, were: $$60,000$ for Corp A$,$ $$180,000$ for Corp B$,$ and $$420,000$ for Corp C$.$

In $2023$ the fair market value of her $100$ common shares were worth $$50,000$ in each of the three corporations.

REQUIRED

a$)$ For each of the three corporations, determine the ACB and PUC of Ms$.$ Chiu$$s common shares.

b$)$ If$,$ in $2023,$ she redeemed her shares of all three corporations for the fair market values, what income would she recognize on each of the three transactions?