Beau Dawson and Willow McDonald formed a partnership, investing $$67,500$ and $$202,500,$ respectively.

Determine their participation in the year's net income of $$300,000$ under each of the following independent assumptions:

a$.$ No agreement concerning division of net income.

b$.$ Divided in the ratio of original capital investment.

c$.$ Interest at the rate of $5\%$ allowed on original investments and the remainder divided in the ratio of $2$:$3.$

d$.$ Salary allowances of $$40,000$ and $$50,000,$ respectively, and the balance divided equally.

e$.$ Allowance of interest at the rate of $5\%$ on original investments, salary allowances of $$40,000$ and $$50,000,$ respectively, and the remainder divided equally.