Step 1: Find what part of the year's sales has passed.
Sales before B's death are Rs 75,000 out of a full year's Rs 4,00,000. The fraction is
\[ \frac{75{,}000}{4{,}00{,}000} = \frac{3}{16} \]
Step 2: Pick the profit to be used.
The sales method takes the profit of the immediately previous year, which is Rs 50,000 for 2024-25. The older years 2022-23 and 2023-24 are not needed.
Step 3: Apply the fraction.
\[ 50{,}000 \times \frac{3}{16} = \frac{1{,}50{,}000}{16} = 9{,}375 \]
Step 4: Cross check with the options.
A time based estimate on Rs 50,000 for three months would be Rs 12,500, which is not offered. The sales based figure Rs 9,375 is present in the options.
Step 5: Conclude.
Profit from April 1, 2025 to June 30, 2025 is Rs 9,375.
\[ \boxed{\text{Rs } 9{,}375} \]
Final Answer:
The profit up to the date of death is Rs 9,375.