Division returns within fixed percentage in a financial game.

Question

There is a game in which there are two types of member one who hold membership(X) and another who does not hold membership(Y). Membership is a stake out of total stakes which is S

I am trying to calculate the returns of the both member within the fixed percentage of returns lets say R = 10% on the total investment.

N as number of Investor.

Every member and non-member invest money(M) using S like

1. Calculating Stake ownership percentage P using S/Total Stake
2. Returning normal distribution T using for everyone R/N .
3. Then adding (P + T)* X + (P + T)*Y = R

But as my values in P changes it goes beyond R.

Any direction ?

You can see my edits I have come so far on my own before down voting.