SOLUTION: Costa starts a company with $2,400,000. After 6 months, he is joined by Luiz, who contributes $3,000,000 in capital. Two months later Costa and Luiz are joined by Paul, who contri

Algebra ->  Proportions -> SOLUTION: Costa starts a company with $2,400,000. After 6 months, he is joined by Luiz, who contributes $3,000,000 in capital. Two months later Costa and Luiz are joined by Paul, who contri      Log On


   

Question 1134834: Costa starts a company with $2,400,000. After 6 months, he is joined by Luiz, who contributes $3,000,000 in capital. Two months later Costa and Luiz are joined by Paul, who contributes $3,300,000. Of the profit accruing a year after Costa had started operations, Costa receives 20% as manager and Paul receives 4% as assistant manager. The remaining profits are then shared in the ratio of the product of their holding in the company and the time elapsing since each of them joined the company. If the profit at the end of the first year was $1,050,000, calculate the total amount received by each of the three partners in the company.
Answer by VFBundy(438) About Me  (Show Source):
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The total profit is $1,050,000. From this, we take off 20% for Costa and 4% for Paul.

Costa = 0.20 * $1,050,000 = $210,000
Paul = 0.04 * $1,050,000 = $42,000

This means there is a remaining profit of $798,000.

It says we are to share the remaining profits "in the ratio of the PRODUCT of their holding in the company and the time elapsing since each of them joined the company." This means we are to multiply the amount of their investments by the amount of their time in the company. At this point, it has been one year (12 months) since the company started. (I'll use months as the time reference.) Costa started the company, so he has been there all 12 months. Luiz joined him six months later, so he has been there six months. Two months after that, Paul joined them, so he has been there four months.

You should note that the following results will not be dollar amounts, but a value representing their overall share in the company. (Dollars invested MULTIPLIED by months of service.) To make the math a little more manageable, we will change the dollar amounts to millions of dollars.

Costa = $2.4M invested * 12 months = 28.8
Luiz = $3M invested * 6 months = 18
Paul = $3.3M * 4 months = 13.2

So, the remaining $798,000 profits are to be split in this ratio:

Costa = 28.8%2F%2828.8%2B18%2B13.2%29 = 28.8%2F60 = 0.48

Luiz = 18%2F%2828.8%2B18%2B13.2%29 = 18%2F60 = 0.30

Paul = 13.2%2F%2828.8%2B18%2B13.2%29 = 13.2%2F60 = 0.22

Costa receives 48% of the $798,000...or $383,040.

Luiz receives 30% of the $798,000...or $239,400.

Paul receives 22% of the $798,000...or $175,560.

Remember, from earlier, Costa received 20% of the profits ($210,000) for being manager and Paul received 4% of the profits ($42,000) for being assistant manager. We must add these to their above totals.

So, out of the entire $1,050,000 profit, it will be split as follows:

Costa = $593,040 ($383,040, plus $210,000 for being manager)

Luiz = $239,400

Paul = $217,560 ($175,560, plus $42,000 for being assistant manager)