Black and Shannon have decided to form a partnership. They have agreed that Black is to invest $$177,000$ and that Shannon is to invest $$59,000.$ Black is to devote one$-$half time to the business, and Shannon is to devote full time. The following plans for the division of income are being considered:

Equal division.

In the ratio of original investments.

In the ratio of time devoted to the business.

Interest of $6\%$ on original investments and the remainder equally.

Interest of $6\%$ on original investments, salary allowances of $$45,000$ to Black and $$80,000$ to Shannon, and the remainder equally.

Plan $($e$),$ except that Shannon is also to be allowed a bonus equal to $20\%$ of the amount by which net income exceeds the total salary allowances.