Watts and Lyon are forming a partnership. Watts invests $$40,500$ and Lyon invests $$49,500.$ The partners agree that Watts will work one$-$fourth of the total time devoted to the partnership and Lyon will work three$-$fourths. They have discussed the following alternative plans for sharing income and loss: $($a$)$ in the ratio of their initial capital investments; $($b$)$ in proportion to the time devoted to the business; $($c$)$ a salary allowance of $$21,000$ per year to Lyon and the remaining balance in accordance with the ratio of their initial capital investments; or $($d$)$ a salary allowance of $$21,000$ per year to Lyon, $10\%$ interest on their initial capital investments, and the remaining balance shared equally. The partners expect the business to perform as follows: Year $1,$ $$19,000$ net loss; Year $2,$ $$47,500$ net income; and Year $3,$ $$79,167$ net income.