A and B entered into a partnership by investing Rs. 40,000 and Rs. 60,000 respectively. At the end of 6 months, A added Rs. 10,000 while B withdrew Rs. 10,000. If the total profit at the end of the year was Rs. 72,000, what is A's share of the profit?

The correct option is Rs. 30,000.

Step 1: Understand the Investment Details
A and B start a business partnership with initial investments for the first 6 months, after which both change their invested amounts for the remaining 6 months of the year.

Step 2: Calculate the Equivalent Monthly Investment for A
For the first 6 months, A invests Rs. 40,000.

$\text{Investment for first 6 months}=40000\times 6=\text{Rs.}240000$
At the end of 6 months, A adds Rs. 10,000, making A's investment Rs. 50,000 for the remaining 6 months.

$\text{Investment for next 6 months}=50000\times 6=\text{Rs.}300000$
Total equivalent 1-month investment of A:

$\text{Total for A}=240000+300000=\text{Rs.}540000$

Step 3: Calculate the Profit Sharing Ratio
Considering the final ratio of investment for A and B to share the total annual profit:

$\text{Ratio of A's share}=\frac{5}{12}$

Step 4: Calculate A's Share of the Total Profit
The total profit at the end of the year is Rs. 72,000.

$\text{A's share of profit}=\frac{5}{12}\times 72000$

$\text{A's share of profit}=5\times 6000=\text{Rs.}30000$

Therefore, A's share of the profit is Rs. 30,000.