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Sagot :
Let's work through the solution step-by-step to derive the required journal entries and the balance sheet of the newly constituted firm, and to determine the sacrificing ratio.
### Step 1: Initial Setup
Given:
- Sundry Creditors: ₹20,000
- Capital Accounts:
- Vimal: ₹60,000
- Nirmal: ₹32,000
- Profit & Loss A/c: ₹20,000
- Cash: ₹14,000
- Debtors: ₹18,000
- Plant & Machinery: ₹50,000
- Stock: ₹40,000
- Goodwill: ₹10,000
### Step 2: New Partner's Introduction
Kailash introduces:
- Capital: ₹40,000
- Goodwill: ₹20,000
### Step 3: Revaluation of Assets
1. Plant & Machinery reduced to ₹35,000 (from ₹50,000).
2. Stock reduced by 10%:
- New Stock = ₹40,000 - (10% of ₹40,000) = ₹40,000 - ₹4,000 = ₹36,000.
3. Provision for bad debts:
- New Debtors = ₹18,000 - ₹1,000 (provision) = ₹17,000.
### Step 4: New Profit Sharing Ratio
New profit-sharing ratio: Vimal : Nirmal : Kailash = 2 : 1 : 1.
### Step 5: Calculating Sacrificing Ratio
The old ratio between Vimal and Nirmal was 3:2, and the new ratio is 2:1:1.
To find the sacrificing ratio, we calculate the difference in the old and new ratios:
1. Old Ratio = [3/5, 2/5]
2. New Ratio for Vimal and Nirmal out of total (4 parts) = [2/4, 1/4]
Sacrificing ratio for each partner:
- Vimal's Sacrifice = (3/5) - (2/4) = 0.6 - 0.5 = 0.1
- Nirmal's Sacrifice = (2/5) - (1/4) = 0.4 - 0.25 = 0.15
So the sacrificing ratio is: Vimal : Nirmal = 0.1 : 0.15.
### Step 6: Goodwill Adjustment
Goodwill paid by Kailash = ₹20,000.
- Vimal's share of goodwill (₹20,000 × 0.1) = ₹2,000
- Nirmal's share of goodwill (₹20,000 × 0.15) = ₹3,000
### Step 7: Adjustments in Capital Accounts
1. Vimal's new capital:
- Initial Capital = ₹60,000
- Adjusted with Goodwill = ₹60,000 + ₹2,000 = ₹62,000
2. Nirmal's new capital:
- Initial Capital = ₹32,000
- Adjusted with Goodwill = ₹32,000 + ₹3,000 = ₹35,000
### Step 8: New Balance Sheet
#### Revalued Assets:
- Cash: ₹14,000
- Debtors (Net of provision): ₹17,000
- Plant & Machinery: ₹35,000
- Stock: ₹36,000
- Goodwill: ₹10,000 + ₹20,000 (from Kailash) = ₹30,000
#### Liabilities:
- Sundry Creditors: ₹20,000
- Vimal's Capital after Goodwill: ₹62,000
- Nirmal's Capital after Goodwill: ₹35,000
- Kailash's Capital: ₹40,000
Total Assets:
[tex]\[ ₹14,000 + ₹17,000 + ₹35,000 + ₹36,000 + ₹30,000 = ₹1,32,000 \][/tex]
Total Liabilities:
[tex]\[ ₹20,000 + ₹62,000 + ₹35,000 + ₹40,000 = ₹1,57,000 \][/tex]
Finally, the details are as follows:
Revalued Assets:
- Cash: ₹14,000
- Debtors (Net of Provision): ₹17,000
- Plant & Machinery: ₹35,000
- Stock: ₹36,000
- Goodwill: ₹30,000
Liabilities:
- Sundry Creditors: ₹20,000
- Vimal's Capital after Goodwill: ₹62,000
- Nirmal's Capital after Goodwill: ₹35,000
- Kailash's Capital: ₹40,000
Total Assets: ₹1,52,000
Total Liabilities: ₹1,57,000
Sacrificing Ratio: Vimal : Nirmal = 0.1 : 0.15
### Step 1: Initial Setup
Given:
- Sundry Creditors: ₹20,000
- Capital Accounts:
- Vimal: ₹60,000
- Nirmal: ₹32,000
- Profit & Loss A/c: ₹20,000
- Cash: ₹14,000
- Debtors: ₹18,000
- Plant & Machinery: ₹50,000
- Stock: ₹40,000
- Goodwill: ₹10,000
### Step 2: New Partner's Introduction
Kailash introduces:
- Capital: ₹40,000
- Goodwill: ₹20,000
### Step 3: Revaluation of Assets
1. Plant & Machinery reduced to ₹35,000 (from ₹50,000).
2. Stock reduced by 10%:
- New Stock = ₹40,000 - (10% of ₹40,000) = ₹40,000 - ₹4,000 = ₹36,000.
3. Provision for bad debts:
- New Debtors = ₹18,000 - ₹1,000 (provision) = ₹17,000.
### Step 4: New Profit Sharing Ratio
New profit-sharing ratio: Vimal : Nirmal : Kailash = 2 : 1 : 1.
### Step 5: Calculating Sacrificing Ratio
The old ratio between Vimal and Nirmal was 3:2, and the new ratio is 2:1:1.
To find the sacrificing ratio, we calculate the difference in the old and new ratios:
1. Old Ratio = [3/5, 2/5]
2. New Ratio for Vimal and Nirmal out of total (4 parts) = [2/4, 1/4]
Sacrificing ratio for each partner:
- Vimal's Sacrifice = (3/5) - (2/4) = 0.6 - 0.5 = 0.1
- Nirmal's Sacrifice = (2/5) - (1/4) = 0.4 - 0.25 = 0.15
So the sacrificing ratio is: Vimal : Nirmal = 0.1 : 0.15.
### Step 6: Goodwill Adjustment
Goodwill paid by Kailash = ₹20,000.
- Vimal's share of goodwill (₹20,000 × 0.1) = ₹2,000
- Nirmal's share of goodwill (₹20,000 × 0.15) = ₹3,000
### Step 7: Adjustments in Capital Accounts
1. Vimal's new capital:
- Initial Capital = ₹60,000
- Adjusted with Goodwill = ₹60,000 + ₹2,000 = ₹62,000
2. Nirmal's new capital:
- Initial Capital = ₹32,000
- Adjusted with Goodwill = ₹32,000 + ₹3,000 = ₹35,000
### Step 8: New Balance Sheet
#### Revalued Assets:
- Cash: ₹14,000
- Debtors (Net of provision): ₹17,000
- Plant & Machinery: ₹35,000
- Stock: ₹36,000
- Goodwill: ₹10,000 + ₹20,000 (from Kailash) = ₹30,000
#### Liabilities:
- Sundry Creditors: ₹20,000
- Vimal's Capital after Goodwill: ₹62,000
- Nirmal's Capital after Goodwill: ₹35,000
- Kailash's Capital: ₹40,000
Total Assets:
[tex]\[ ₹14,000 + ₹17,000 + ₹35,000 + ₹36,000 + ₹30,000 = ₹1,32,000 \][/tex]
Total Liabilities:
[tex]\[ ₹20,000 + ₹62,000 + ₹35,000 + ₹40,000 = ₹1,57,000 \][/tex]
Finally, the details are as follows:
Revalued Assets:
- Cash: ₹14,000
- Debtors (Net of Provision): ₹17,000
- Plant & Machinery: ₹35,000
- Stock: ₹36,000
- Goodwill: ₹30,000
Liabilities:
- Sundry Creditors: ₹20,000
- Vimal's Capital after Goodwill: ₹62,000
- Nirmal's Capital after Goodwill: ₹35,000
- Kailash's Capital: ₹40,000
Total Assets: ₹1,52,000
Total Liabilities: ₹1,57,000
Sacrificing Ratio: Vimal : Nirmal = 0.1 : 0.15
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