### Step-by-Step Solution:
1. Initial Balance Sheet Values:
- Sundry Creditors: ₹13,590
- Cash: ₹5,900
- Debtors: ₹8,000
- Stock: ₹11,690
- Buildings: ₹23,000
- Capital A: ₹15,000
- Capital B: ₹10,000
- Capital C: ₹10,000
2. Building Appreciation:
Buildings' value appreciated by ₹7,000:
[tex]\[ \text{New Value of Buildings} = ₹23,000 + ₹7,000 = ₹30,000 \][/tex]
3. Provision for Bad Debts:
Provision for bad debts at 5% on Debtors:
[tex]\[ \text{Provision for Bad Debts} = 0.05 \times ₹8,000 = ₹400 \][/tex]
[tex]\[ \text{New Value of Debtors} = ₹8,000 - ₹400 = ₹7,600 \][/tex]
4. Goodwill Adjustment:
Goodwill valued at ₹9,000 to be divided among A, B, and C according to their profit-sharing ratio (3:2:1).
[tex]\[ \text{Goodwill Share of A} = \frac{3}{6} \times ₹9,000 = ₹4,500 \][/tex]
[tex]\[ \text{Goodwill Share of B} = \frac{2}{6} \times ₹9,000 = ₹3,000 \][/tex]
[tex]\[ \text{Goodwill Share of C} = \frac{1}{6} \times ₹9,000 = ₹1,500 \][/tex]
5. Adjust Capital Accounts for Goodwill:
Without raising Goodwill Account:
- A’s Capital will be debited for his share of Goodwill:
[tex]\[ \text{Capital A} = ₹15,000 - ₹4,500 = ₹10,500 \][/tex]
- B’s Capital will be credited for his share of Goodwill and the same amount debited to make net zero effect for B:
[tex]\[ \text{Capital B} \text{ (No effect as balance)} = ₹10,000 \][/tex]
- C’s Capital will be debited for his share of Goodwill:
[tex]\[ \text{Capital C} = ₹10,000 - ₹1,500 = ₹8,500 \][/tex]
6. Payment to B:
₹5,000 paid to B immediately and the balance is treated as a loan:
- Cash will decrease by ₹5,000:
[tex]\[ \text{New Cash Balance} = ₹5,900 - ₹5,000 = ₹900 \][/tex]
- Capital B will be debited by ₹5,000:
[tex]\[ \text{Capital B Balance} = ₹10,000 - ₹5,000 = ₹5,000 \][/tex]
- Remaining balance due to B treated as a loan:
[tex]\[ \text{Loan to B} = ₹5,000 \][/tex]
7. New Balance Sheet Post B's Retirement:
_Assets:_
- Cash: ₹900
- Debtors: ₹7,600
- Less: Provision for Bad Debts: ₹400
- Stock: ₹11,690
- Buildings: ₹30,000
_Total Assets: ₹49,790_
_Liabilities and Capital:_
- Sundry Creditors: ₹13,590
- Capital A: ₹10,500
- Capital C: ₹8,500
- Loan to B: ₹5,000
_Total Liabilities and Capital: ₹49,790_
_Final Values:_
- Sundry Creditors: ₹13,590
- Cash: ₹900
- Debtors: ₹7,600 (after provision ₹400 deduction)
- Stock: ₹11,690
- Buildings: ₹30,000
- Capital A: ₹10,500
- Capital C: ₹8,500
- Loan to B: ₹5,000
Thus, the new Balance Sheet immediately after B's retirement appears as follows:
### New Balance Sheet
[tex]\[
\begin{array}{|c|c|c|c|c|}
\hline
\text{Liabilities} & & \text{₹} & \text{Assets} & \text{₹} \\
\hline
\text{Sundry Creditors} & & 13,590 & \text{Cash} & 900 \\
\hline
\text{Loan to B} & & 5,000 & \text{Debtors} & 7,600 \\
\hline
\text{Capital Accounts:} & & & \text{Less: Provision for Bad Debts} & 400 \\
\hline
\text{A} & 10,500 & & \text{Stock} & 11,690 \\
\hline
\text{C} & 8,500 & & \text{Buildings} & 30,000 \\
\hline
& & 37,590 & & 49,790 \\
\hline
& & 49,790 & & 49,790 \\
\hline
\end{array}
\][/tex]
This shows the final adjustment and values for all accounts involved after B's retirement on 31st December 2005.
