Simplex had incorrectly been using the cash method of accounting. For $2023,$ it voluntarily changed to the accrual method. The adjustment due to the change in method as calculated at the beginning of $2023$ was $$120,000($positive$).$ The adjustment as calculated as of the end of $2023$ was $$80,000($positive$).$ As a result of the change in method, Simplex increases its $2023$ gross income by:

a$.$ $$120,000.$

b$.$ $$40,000.$

c$.$ $$30,000.$

d$.$ $$80,000.$