The problem provides a statement of partners' capitals for M, D, and R Partnership. We are given the beginning capitals, additional investments, net income (loss), partners' drawings, and ending capitals. We are also given information on how the net income (loss) is divided. We need to calculate the missing amount defined by the letter K, which represents Dima's ending capital.

1. Problem Description

The problem provides a statement of partners' capitals for M, D, and R Partnership. We are given the beginning capitals, additional investments, net income (loss), partners' drawings, and ending capitals. We are also given information on how the net income (loss) is divided. We need to calculate the missing amount defined by the letter K, which represents Dima's ending capital.

2. Solution Steps

First, we determine the beginning capital for each partner. The total beginning capital is $120,000$, and the ownership ratio is $1:1:1$. Therefore, each partner's beginning capital is:

$120,000 / 3 = 40,000$.

So, $A = B = C = 40,000$.

Next, we calculate the total additional investment $E$. $E$ is the additional investment by Mahdi plus additional investment by Dima plus additional investment by Raed. We know that Raed made an additional investment of

0. Let D be the additional investment of Dima. We can not find the exact value of $E$ yet.

Then, we determine the total drawings, $I$. Mahdi's drawings are zero, Dima's drawings are $24,000$, and Raed's drawings are $12,000$. So, the total drawings are:

$I = 0 + 24,000 + 12,000 = 36,000$.

Now, we use the total ending capitals to find the total additional investment. The fundamental accounting equation applied to the partnership as a whole is:

Beginning Capitals + Additional Investment + Net Income (Loss) - Drawings = Ending Capitals

$120,000 + E + (-42,000) - 36,000 = 77,000$

$120,000 + E - 42,000 - 36,000 = 77,000$

$E + 42,000 = 77,000$

$E = 77,000 - 42,000$

$E = 35,000$.

So, the total additional investment is $35,

0

0

0. Since Mahdi invested $25,000 and Raed invested $0, Dima's additional investment is $35,000 - 25,000 - 0 = 10,000$. So $D = 10,000$.

Next, we calculate Dima and Raed's salaries. Dima's salary is $5\%$ of her beginning capital, and Raed's salary is $5\%$ of his beginning capital.

Dima's Salary = $0.05 * 40,000 = 2,000$

Raed's Salary = $0.05 * 40,000 = 2,000$

Dima and Raed withdrew an amount equal to their salaries. So, Dima's drawings are $24,000$, which implies her salary is also $24,

0

0

0.

The total salaries = Dima's Salary + Raed's Salary. The remaining income (loss) is allocated equally between the three partners.

Now we know that Dima and Raed withdraw exactly their salaries, and this is $24,000$ and $12,000$ respectively. This gives us information about the salaries allocated to Dima and Raed. Dima withdrew $24,000$, so Dima's salary is $24,000$. Raed withdrew $12,000$, so Raed's salary is $12,000$.

The interest expense is $0.05 \times 40,000 \times 3 = 6,000$.

The total salaries are $24,000 + 12,000 = 36,000$.

The remaining net loss is $(-42,000 - (-6,000) - 36,000) = -42,000 + 6,000 - 36,000 = -72,000$.

The loss allocated equally to the three partners is $-72,000 / 3 = -24,000$.

Mahdi's share of net income = Interest + Share of Remaining Income = $0 + (-24,000) = -24,000$.

Dima's share of net income = Interest + Salary + Share of Remaining Income = $2,000 + 24,000 - 24,000 = 2,000$. Wait - Dima's Salary is 24000, not 2000!

Interest Expense = 0.05 \times \40,000 \times 3 = \$6,000$

Salaries = \24,000 + \12,000 = \36,000$

Total expenses to be allocated = \6,000 + \36,000 = \42,000$

Since the partnership incurred a loss of \42,000$, and all the expenses exactly consume the loss, there is nothing remaining to be divided between the partners.

Mahdi's net income = Interest + Salary + Equal Share $= 0 + 0 + 0 = 0$

Dima's net income = Interest + Salary + Equal Share $= 2,000 + 24,000 + 0 = 26,000$. However, interest is $5\% * 40,000 = 2,000$, but salary is $24,000$.

Raed's net income = Interest + Salary + Equal Share $= 2,000 + 12,000 + 0 = 14,000$.

Mahdi's Ending Capital = $40,000 + 25,000 + F - 0 = J$. F is Mahdi's share of net income, which is

0. So $J = 65,000$

Dima's Ending Capital = $40,000 + 10,000 + G - 24,000 = K$. G is Dima's share of net income, which is $26,000 + equal share$. Then $K = 40,000 + 10,000 + 26,000 - 24,000 = 52,000$

Raed's Ending Capital = $40,000 + 0 + H - 12,000 = L$. Raed's net income is $14,000$. $L = 40,000 + 14,000 - 12,000 = 42,000$

Now, summing the ending capitals, $65,000 + K + L = 77,000$. $65,000 + K + L = 77,000$, therefore $K + L = 12,000$.

We know Raed has $14,000$ from beginning capital + interest +salary +equal share, and withdrawals are $12,000$ .

$77,000 = 65,000 + K + L$, so $K + L = 12,000$

We calculate K now.

$K = 40,000 (\text{Beginning}) + 10,000 (\text{Investment}) + 26,000 (\text{Net Income}) - 24,000 (\text{Drawings}) = 52,000$.

3. Final Answer

52000