L and M are partners sharing profits in the ratio $3:2$. N is admitted as a partner for $\frac{1}{5}\text{th}$ of the share which is acquired entirely from L. Goodwill of the firm is valued at $\text{Rs. }40,000$ on N's admission. N will have to pay for Goodwill:

Let's calculate the value of premium for goodwill brought by N and how it is distributed:1. Calculate N's share of Goodwill:
$$\text{Total firm Goodwill}=\text{Rs. }40,000$$
$$\text{N’s share of Goodwill}=40,000\times \frac{1}{5}=\text{Rs. }8,000$$
2. Allocation based on Sacrifice:Since N acquires his entire share exclusively from L, L is the sole sacrificing partner, while M sacrifices nothing ($0$). Premium for goodwill is compensated only to sacrificing partners. Therefore, the entire $\text{Rs. }8,000$ must be given to L.