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 answer is 2200.

Step-by-Step Explanation:

In a partnership business, the profit shared between partners is directly proportional to the product of their investment amounts and the time periods for which those investments were held.

Step 1: Determine the investment and duration for each person.
Person A's investment = Rs 4000 for 12 months (entire year).
Person B's investment = Rs 6000 for 8 months.

Step 2: Calculate the ratio of their profit shares.
Ratio of profit of A to B = (A's investment × A's time) : (B's investment × B's time)

$\text{Ratio}=(4000\times 12):(6000\times 8)$

$\text{Ratio}=48000:48000$

Simplifying the ratio:

$\text{Ratio}=1:1$

Step 3: Calculate A's share of the total profit.
Total profit = Rs 4400.
Since the ratio of their shares is 1 : 1, total ratio units = 1 + 1 = 2 units.

$\text{A's Share}=\frac{1}{2}\times 4400=2200$

Therefore, the share of profit for A is Rs 2200.