Q. 50. Vimal and Nirmal are partners sharing profits in the ratio of [tex][tex]$3:2$[/tex][/tex]. The following was the position of their business as of 31st March, 2022:

\begin{tabular}{|c|c|c|c|}
\hline
Liabilities & ₹ & Assets & ₹ \\
\hline
Sundry Creditors & 20,000 & Cash & 14,000 \\
\hline
Capital Accounts: & & Debtors & 18,000 \\
\hline
Vimal & 60,000 & Plant \& Machinery & 50,000 \\
\hline
Nirmal & 32,000 & Stock & 40,000 \\
\hline
Profit \& Loss A/c & 20,000 & Goodwill & 10,000 \\
\hline
& 1,32,000 & & 1,32,000 \\
\hline
\end{tabular}

On 1st April, 2022, Kailash agrees to join the business on the following terms and conditions:
1. He will introduce [tex]₹ 40,000[/tex] as his capital and pay [tex]₹ 20,000[/tex] to the existing partners for his share of goodwill.
2. The new profit-sharing ratio will be [tex]2:1:1[/tex] respectively for Vimal, Nirmal, and Kailash.
3. A revaluation of assets will be made by reducing plant and machinery to [tex]₹ 35,000[/tex] and stock by [tex]10\%[/tex]. Provision of [tex]₹ 1,000[/tex] is to be created for bad and doubtful debts.

Pass journal entries for the above arrangements and give the balance sheet of the newly constituted firm. Also, specify the sacrificing ratio.

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