A and B share profits in the ratio of $3:2$. C was admitted as a partner who gets $\frac{1}{5}$ share. New profit sharing ratio, if C acquires $\frac{3}{20}$ from A and $\frac{1}{20}$ from B, would be:

Let's calculate the new shares step-by-step:Old Shares: $\text{A}=\frac{3}{5},\text{B}=\frac{2}{5}$ Sacrifice by A to C = $\frac{3}{20}$ Sacrifice by B to C = $\frac{1}{20}$ New Share of A:
$$\text{New Share}=\text{Old Share}-\text{Sacrifice}$$
$$\text{A}=\frac{3}{5}-\frac{3}{20}=\frac{12-3}{20}=\frac{9}{20}$$
New Share of B:
$$\text{B}=\frac{2}{5}-\frac{1}{20}=\frac{8-1}{20}=\frac{7}{20}$$
Share of C:
$$\text{C}=\frac{1}{5}=\frac{4}{20}$$
Combining these, the new profit sharing ratio among A, B, and C is $9:7:4$.