The current profit-sharing ratio between R and S is 4:1. Upon T's admission, T will receive 1/5 of the total share, which will be divided equally between R and S.
- T's allocated share is \( \frac{1}{5} \).
The remaining share to be distributed between R and S is \( 1 - \frac{1}{5} = \frac{4}{5} \).
This remaining \( \frac{4}{5} \) share is to be divided between R and S in their existing ratio of 4:1.
The sum of the ratio parts is \( 4 + 1 = 5 \).
R's new share is calculated as:
\[\frac{4}{5} \times \frac{4}{5} = \frac{16}{25}\]
S's new share is calculated as:
\[\frac{1}{5} \times \frac{4}{5} = \frac{4}{25}\]
Consequently, the new profit-sharing ratio among R, S, and T is:
\[R : S : T = \frac{16}{25} : \frac{4}{25} : \frac{1}{5} = 16 : 4 : 5\]
The revised profit-sharing ratio is therefore 16:4:5.