A and B are partners sharing profits in the ratio of 2:1. C is admitted into the firm for 1/4 share of profits. C brings in Rs. 20,000 in respect of his capital. The capitals of old partners A and B, after all adjustments relating to goodwill, revaluation of assets and liabilities, etc., are Rs. 45,000 and Rs. 15,000 respectively. It is agreed that partners' capitals should be according to the new profit sharing ratio. Determine the new profit sharing ratio

To find the new profit sharing ratio, we calculate the remaining share after allocating C's share: Let total profit share of the firm be $1$.Given C's profit share = $\frac{1}{4}$ The remaining share available for A and B is:
$$\text{Remaining Share}=1-\frac{1}{4}=\frac{3}{4}$$
Unless specified otherwise, the old partners share this remaining profit pool in their historical mutual profit-sharing ratio of $2:1$.Calculate the new shares for A and B:
$$\text{A’s New Share}=\frac{2}{3}\times \frac{3}{4}=\frac{6}{12}=\frac{2}{4}$$
$$\text{B’s New Share}=\frac{1}{3}\times \frac{3}{4}=\frac{3}{12}=\frac{1}{4}$$
Express all shares with a common denominator of $4$:A's Share = $\frac{2}{4}$ B's Share = $\frac{1}{4}$ C's Share = $\frac{1}{4}$ Thus, the New Profit Sharing Ratio is $2:1:1$. Note that the extra information provided regarding capital balances is superfluous for computing the ratio itself.