Let's prepare the detailed solution step-by-step:
### Step 1: Calculation of Firm's Goodwill and Virat's Share in Goodwill
Goodwill is valued at three times the average profit of the last four years.
Last Four Years' Profits:
- Year I: ₹ 30,000
- Year II: ₹ 25,000
- Year III: ₹ 25,000
- Year IV: ₹ 40,000
Average Profit:
[tex]\[
\text{Average Profit} = \frac{(30000 + 25000 + 25000 + 40000)}{4} = \frac{120000}{4} = ₹ 30,000
\][/tex]
Goodwill of the Firm:
[tex]\[
\text{Goodwill} = 30,000 \times 3 = ₹ 90,000
\][/tex]
Virat's Share of Goodwill (Profit Sharing Ratio 7:5:4):
[tex]\[
\text{Virat's Share} = \frac{4}{16} \times 90,000 = \frac{1}{4} \times 90,000 = ₹ 22,500
\][/tex]
### Step 2: Calculation of Profit Up to the Date of Death
Profit up to the date of death is calculated based on last year's profit. Virat died on 30th June 2017, so we need to calculate the profit for 3 months (April, May, June).
Last Year’s Profit:
[tex]\[
\text{Profit} = ₹ 40,000 \quad (for 12 months)
\][/tex]
Monthly Profit:
[tex]\[
\text{Monthly Profit} = \frac{40,000}{12} = ₹ 3,333.33
\][/tex]
Profit for 3 Months:
[tex]\[
\text{Profit for 3 months} = 3,333.33 \times 3 = ₹ 10,000
\][/tex]
Virat's Share of Profit:
[tex]\[
\text{Virat’s Share} = \frac{4}{16} \times 10,000 = \frac{1}{4} \times 10,000 = ₹ 2,500
\][/tex]
### Step 3: Calculation of Virat's Salary
Virat was entitled to a salary of ₹ 1200 per month.
Salary for 3 months (April, May, June):
[tex]\[
\text{Salary} = 1200 \times 3 = ₹ 3,600
\][/tex]
### Step 4: Calculation of Interest on Capital
Interest on capital is to be allowed at 10% per annum. However, Virat’s initial capital is not given, so we will assume it as zero.
Interest on Capital:
[tex]\[
\text{Interest} = \text{Initial Capital} \times \frac{10}{100} \times \frac{3}{12} = 0 \times 0.10 \times 0.25 = ₹ 0
\][/tex]
### Step 5: Calculation of Virat's Drawing Up to the Date of Death
Virat’s drawings were ₹ 900 per month.
Drawings for 3 months (April, May, June):
[tex]\[
\text{Drawing} = 900 \times 3 = ₹ 2,700
\][/tex]
### Step 6: Calculation of Final Amount Payable
[tex]\[
\text{Total Payable} = \text{Virat's Share of Goodwill} + \text{Virat's Share of Profit} + \text{Salary} + \text{Interest on Capital} - \text{Drawing}
\][/tex]
Substitute the calculated values:
[tex]\[
\text{Total Payable} = 22,500 + 2,500 + 3,600 + 0 - 2,700 = ₹ 25,900
\][/tex]
### Summary of the Calculations:
- Average Profit: ₹ 30,000
- Goodwill: ₹ 90,000
- Virat's Share in Goodwill: ₹ 22,500
- Profit for 3 Months: ₹ 10,000
- Virat's Share of Profit: ₹ 2,500
- Salary for 3 Months: ₹ 3,600
- Interest on Capital: ₹ 0
- Drawings for 3 Months: ₹ 2,700
- Amount Payable to Virat's Executor: ₹ 25,900
The final amount payable to Virat’s executor is ₹ 25,900.
