### Solution
#### Step 1: Calculation of Raina's Capital Contribution
- Raina is admitted with a \(\frac{1}{6}\) share in the profits.
- Raina will bring \(₹ 40,000\) as her capital.
#### Step 2: Adjusting Capitals of Badal and Bijli
- The total capital of the firm after Raina's admission should equate with her \(\frac{1}{6}\) share.
- Therefore, the firm's total capital will be:
[tex]\[
\text{Total Capital} = ₹ 40,000 \times 6 = ₹ 240,000
\][/tex]
- Raina’s capital is \( \frac{1}{6} \times ₹ 240,000 = ₹ 40,000 \).
- This implies Badal and Bijli will share the remaining ₹ 200,000 between them.
#### Step 3: Goodwill Adjustment
- Raina will bring goodwill premium of ₹ 12,000 in cash.
- Goodwill should be divided between Badal and Bijli in their old profit-sharing ratio.
Assuming the old ratio is 1:1:
- Badal's share = \(\frac{12,000}{2} = ₹ 6,000\)
- Bijli's share = \(\frac{12,000}{2} = ₹ 6,000\)
#### Step 4: Revaluation Account Adjustments
1. Building Revaluation:
- Increased by ₹ 15,000
2. Stock Revaluation:
- Increased by ₹ 3,000
Total increment in asset value:
[tex]\[
₹ 15,000 + ₹ 3,000 = ₹ 18,000
\][/tex]
#### Step 5: Provision for Bad Debts
- A provision of \(10\%\) is to be created on debtors for bad debts.
Assuming debtors amount before provision:
Let’s assume debtors amount is \( ₹ 50,000 \).
- Provision for bad debt = \(10\% \text{ of } ₹ 50,000 = ₹ 5,000\)
#### Summary of Adjustments:
- Building and stock revaluation increase the assets by ₹ 18,000.
- Provision for bad debts decrease the asset by ₹ 5,000.
#### Net Impact on Equity:
- Net revaluation impact:
[tex]\[
₹ 18,000 - ₹ 5,000 = ₹ 13,000
\][/tex]
- Adjust this net revaluation gain among Badal and Bijli equally, assuming old ratio is 1:1:
[tex]\[
\text{Each partner's share} = \frac{₹ 13,000}{2} = ₹ 6,500
\][/tex]
### Final Adjustments in Capitals
- Badal's Capital after adjustment:
[tex]\[
\text{Old Capital} + Goodwill share + Revaluation gain
\][/tex]
Assume Badal's capital before adjustments = \( B \).
Here's the updated calculation:
[tex]\[
B + ₹ 6,000 + ₹ 6,500 = B + ₹ 12,500
\][/tex]
- Bijli's Capital after adjustment:
Similarly, let Bijli's capital before adjustments = \( J \).
[tex]\[
J + ₹ 6,000 + ₹ 6,500 = J + ₹ 12,500
\][/tex]
### Current Account Adjustments
- Both Badal and Bijli’s current accounts will be adjusted so the sum of their capitals matches the recalculated value after Raina’s entry.
This detailed explanation aligns the admission of a new partner and the corresponding adjustments in the balance sheet per the given terms.
