Das and Sinha are partners in a firm sharing profits in a $4:1$ ratio. They admitted Pal as a new partner for $\frac{1}{4}\text{th}$ share in the profits, which he acquired wholly from Das. The new profit sharing ratio of the partners is:

Let's calculate the new shares step-by-step:Old shares:
$$\text{Das}=\frac{4}{5},\text{Sinha}=\frac{1}{5}$$
Pal's new share = $\frac{1}{4}$ Since Pal acquires his share wholly from Das, we deduct $\frac{1}{4}$ from Das's share, while Sinha's share remains unchanged.Das's New Share:
$$\text{Das’s New Share}=\frac{4}{5}-\frac{1}{4}=\frac{16-5}{20}=\frac{11}{20}$$
Sinha's New Share:
$$\text{Sinha’s New Share}=\frac{1}{5}=\frac{1\times 4}{5\times 4}=\frac{4}{20}$$
Pal's New Share:
$$\text{Pal’s New Share}=\frac{1}{4}=\frac{1\times 5}{4\times 5}=\frac{5}{20}$$
The new profit-sharing ratio (Das : Sinha : Pal) is $\frac{11}{20}:\frac{4}{20}:\frac{5}{20}⟹11:4:5$.