$A$ and $N$ are partners sharing profits in the ratio $2:1$. $A$ 's son $Ashu$ was admitted as a partner for $\frac{1}{4}\text{th}$ share, half of which was gifted by $A$ to her son. The remaining portion was contributed by $N$. The goodwill of the firm is valued at Rs. $40,000$. How much amount will be credited to the old partners' capital accounts respectively for goodwill?

Let's find the incoming premium value and the individual sacrifice distributions:Total Value of Firm Goodwill: Rs. $40,000$ Ashu's Share of profit: $\frac{1}{4}$ Total Goodwill due from Ashu: $40,000\times \frac{1}{4}=\text{Rs. }10,000$ Now, find out how much share each partner surrendered (Sacrificing ratio):Share given by $A=\text{Half of }\frac{1}{4}=\frac{1}{4}\times \frac{1}{2}=\frac{1}{8}$ Share given by $N=\text{Remaining half}=\frac{1}{4}\times \frac{1}{2}=\frac{1}{8}$ Since both $A$ and $N$ are sacrificing an equal share ($\frac{1}{8}$ each), their Sacrificing Ratio is equal ($1:1$).The premium of Rs. 10,000 must be divided equally between them:
$$\text{Goodwill credited to }A=10,000\times \frac{1}{2}=\text{Rs. }5,000$$
$$\text{Goodwill credited to }N=10,000\times \frac{1}{2}=\text{Rs. }5,000$$