Two persons A and B started a partnership. A invested Rs 4000 for the entire year, while B invested Rs 6000 for 8 months. If the total profit at the end of the year is Rs 4400, then find the share of profit A (in Rs).

The correct option is 2200.

Step 1: Concept of Partnership Profit Share
In a business partnership, the total profit earned at the end of a given period is divided among the partners in proportion to the product of their investment amounts and their respective time durations.
$\text{Profit Ratio of A to B}=({\text{Investment}}_{\mathrm{A}}\times {\text{Time}}_{\mathrm{A}}):({\text{Investment}}_{\mathrm{B}}\times {\text{Time}}_{\mathrm{B}})$

Step 2: Calculate the Equivalent Investment for A and B
For Person A:
Amount invested = Rs 4000
Time period = Entire year = 12 months
$\text{Equivalent Investment of A}=4000\times 12=48000$

For Person B:
Amount invested = Rs 6000
Time period = 8 months
$\text{Equivalent Investment of B}=6000\times 8=48000$

Step 3: Find the Ratio of Profit Sharing
The ratio of the profit shared between A and B is:
$\text{Ratio (A : B)}=48000:48000=1:1$

Step 4: Calculate Person A's Share
Total profit at the end of the year = Rs 4400
Total ratio parts = 1 + 1 = 2
A's share of the profit:
$\text{Share of A}=\frac{1}{2}\times 4400=2200$

Hence, the share of profit of A is Rs 2200.