Step 1: Understanding the Concept:
When a partner dies mid-year, they are entitled to a share of the firm's profit for the period they were alive in the current year. This is usually calculated on a Time Basis using past profits as a benchmark.
Step 2: Key Formula or Approach:
1. Calculate the Average Profit of the specified previous years.
2. Determine the Time Period (from the start of the year to the date of death).
3. Calculate the profit for that specific period.
4. Calculate the deceased partner's share based on the Profit Sharing Ratio (PSR).
Step 3: Detailed Explanation:
1. Calculate Average Profit:
\[ \text{Average Profit} = \frac{8,000 + 9,000 + 10,000}{3} = \frac{27,000}{3} = 9,000 \]
2. Determine Time Period:
The firm follows a calendar year (January to December). Joshi died on February 28, 2018.
Months worked in 2018 = 2 months (January and February).
3. Calculate Profit for 2 months:
\[ \text{Estimated Yearly Profit} = 9,000 \]
\[ \text{Profit for 2 months} = 9,000 \times \frac{2}{12} = 1,500 \]
4. Calculate Joshi's Share:
As no PSR is mentioned for Ram, Manohar, and Joshi, they are assumed to share profits equally (1:1:1).
\[ \text{Joshi's Share} = 1,500 \times \frac{1}{3} = 500 \]
Step 4: Final Answer:
Joshi’s share of profit till the date of his death is Rs. 500.
Therefore, the correct option is (a).