A and B entered into a partnership and invested their respective amounts in the ratio of 2: 1. C and D entered into another partnership with initial investment ratio of 2: 1. Total investment of A and B was 25% less than that of C and D. If total profit of all 4 person at the end of year is Rs.10500, then find profit of A.

The correct option is Rs.3000.

Let's find the profit share of A step-by-step:

Step 1: Set up the total investments of the two partnerships.
Let the total investment of C and D be 100x.
Since the total investment of A and B is 25% less than that of C and D, we have:
$\text{Total investment of A and B}=100x-25\%\text{of}100x=75x$

Step 2: Calculate the individual investments of A, B, C, and D.
The investment ratio of A and B is 2 : 1. Therefore:
$\text{Investment of A}=\frac{2}{2+1}\times 75x=\frac{2}{3}\times 75x=50x$
$\text{Investment of B}=\frac{1}{2+1}\times 75x=\frac{1}{3}\times 75x=25x$
The investment ratio of C and D is also 2 : 1. Therefore:
$\text{Investment of C}=\frac{2}{2+1}\times 100x=\frac{200}{3}x$
$\text{Investment of D}=\frac{1}{2+1}\times 100x=\frac{100}{3}x$

Step 3: Determine the profit-sharing ratio among all four partners.
Since all four partners invested for the same duration (1 year), their profit-sharing ratio is directly proportional to their individual investments:
$\text{Ratio of profit shares (A : B : C : D)}=50x:25x:\frac{200}{3}x:\frac{100}{3}x$
Multiplying the entire ratio by 3 and dividing by x to simplify:
$\text{A : B : C : D}=150:75:200:100$
Dividing by 25 to simplify further:
$\text{A : B : C : D}=6:3:8:4$

Step 4: Calculate the profit of A.
Sum of the ratio parts:
$6+3+8+4=21\text{units}$
Given that the total profit is Rs. 10500:
$21\text{units}=\text{Rs.}10500$
$1\text{unit}=\frac{10500}{21}=\text{Rs.}500$
Since A's share is 6 units:
$\text{Profit of A}=6\times 500=\text{Rs.}3000$