**Calculation of New Partner's Profit Sharing Ratio:**

The existing partners, Rao, Ramesh, and Gopal, have a profit sharing ratio of 3:5:2. Now, Darshan is admitted as a new partner, and Sudarshan is bought out by the firm for his capital and goodwill.

1. Calculation of Sudarshan's Share:
- Sudarshan's capital investment = Rs. 40,000
- Sudarshan's share of goodwill = Rs. 30,000
- Sudarshan's total share = Rs. 40,000 + Rs. 30,000 = Rs. 70,000

2. Calculation of New Partner's Share:
- Total capital after the admission of Darshan = Total capital before admission + Capital of new partner
- Total capital after admission = (Rao's capital + Ramesh's capital + Gopal's capital) + Darshan's capital
- Total capital after admission = (3x + 5x + 2x) + Rs. 40,000
- Total capital after admission = 10x + Rs. 40,000

- Now, let's assume Darshan's capital is y.
- Darshan's share of profit = (Darshan's capital / Total capital after admission) * Total profit
- Darshan's share of profit = (y / (10x + Rs. 40,000)) * Total profit

3. Calculation of New Profit Sharing Ratio:
- The new profit sharing ratio will be the ratio of the old profit sharing ratios and the new partner's share of profit.
- New profit sharing ratio = (Old profit sharing ratio) + New partner's share of profit
- New profit sharing ratio = (3:5:2) + (y / (10x + Rs. 40,000)) * Total profit

**General Entry in the Books of the Firm:**

1. When Sudarshan's Capital and Goodwill are Bought Out:
- Sudarshan's capital account is debited and Sudarshan's goodwill account is debited.
- To Darshan's capital account and Darshan's goodwill account.

General Entry:
- Debit: Sudarshan's Capital Account
- Debit: Sudarshan's Goodwill Account
- Credit: Darshan's Capital Account
- Credit: Darshan's Goodwill Account

2. When Darshan is Admitted as a New Partner:
- Darshan's capital account is debited.
- To Darshan's current account.

General Entry:
- Debit: Darshan's Capital Account
- Credit: Darshan's Current Account

3. When Sudarshan's Capital and Goodwill are Paid Off:
- Darshan's capital account is debited and Darshan's goodwill account is debited.
- To Sudarshan's capital account and Sudarshan's goodwill account.

General Entry:
- Debit: Darshan's Capital Account
- Debit: Darshan's Goodwill Account
- Credit: Sudarshan's Capital Account
- Credit: Sudarshan's Goodwill Account

These entries will ensure the proper recording of the admission of Darshan as a new partner and the settlement of Sudarshan's capital and goodwill.