Let's break down the information given step by step:

1. The first brother received \(\frac{1}{3}\) of the profit.

2. The second brother received \(\frac{2}{3}\) of the remainder after the first brother.

3. The third brother received the remaining N12000.00.

Let's assume the total profit is represented by \(P\).

1. First brother received: \(\frac{1}{3}P\) profit.

2. After the first brother, the remaining profit: \(P - \frac{1}{3}P = \frac{2}{3}P\).

3. Second brother received: \(\frac{2}{3} \cdot \frac{2}{3}P = \frac{4}{9}P\) profit.

4. Third brother received: Remaining profit = Total profit - Profit taken by first and second brothers

5. Third brother received: \(P - \left(\frac{1}{3}P + \frac{4}{9}P\right) = P - \frac{7}{9}P = \frac{2}{9}P\).

Given that the third brother received N12000.00, we can set up an equation to solve for the total profit \(P\):

\(\frac{2}{9}P = 12000\)

Multiply both sides by \(\frac{9}{2}\):

\[P = 12000 \cdot \frac{9}{2} = 54000\]