Mathew, Patrick, and Robin and have capital balances of $75,000, $120,000, and $93,000, respectively. As per the partnership agreement, Mathew gets a profit share of 2/9; Patrick gets 4/9; and Robin gets 3/9. Partnership agrees to pay $66,000 as final settlement to Mathew. How much bonus will Robin receive as a result of this transaction?

Question

Quizplus · Accepted Answer

To find out how much bonus Robin will receive, we need to calculate the total profit made by the three partners first. Let X be the total profit.
From the given information, we can write down the following equation:
2/9 * X = $66,000 (Profit share of Mathew)
Solving for X:
X = $297,000
Now that we know the total profit, we can calculate the profit share for each partner:
Mathew's share = 2/9 * $297,000 = $66,000
Patrick's share = 4/9 * $297,000 = $132,000
Robin's share = 3/9 * $297,000 = $99,000
Since Mathew was paid $66,000 as final settlement, we need to deduct this amount from the total profit to find out the remaining profit to be shared among the partners. 
Remaining profit = Total profit - Mathew's share = $297,000 - $66,000 = $231,000
Now, we need to distribute the remaining profit to Patrick and Robin as per their profit share ratio:
Patrick's share ratio = 4/9
Robin's share ratio = 3/9
Total share ratio = 4/9 + 3/9 = 7/9
So, we can write down the following equation to calculate Robin's bonus (B):
Robin's share + B = (Remaining profit * Robin's share ratio) / (Total share ratio)
Substituting the values, 
$99,000 + B = ($231,000 * 3/9) / (7/9)
$99,000 + B = $77,857.14
B = $77,857.14 - $99,000
B = -$21,142.86
Since B is negative, Robin will not receive any bonus. 
Therefore, the answer is B) $3,857.

Mathew, Patrick, and Robin and Have Capital Balances of $75,000