Profit sharing among investors

Question

Abigail, Bart, and Cathy invested \$2,400, \$3,600, and \$6,000 respectively to start a partnership business. At the end of the first year, the business earned a profit of 40% on the initial investment. The profit was taxed at the rate of 30%. The three investors shared the remaining profit, in amounts proportionate to their original investments. What was Cathy’s share of the remaining profit?

Answer 1

We give an outline of the calculation.

(1) The total investment was $12000$. So what was the profit, in dollars?

(2) After we pay the $30\%$ tax, how much of the profit calculated in (1) remains to be distributed?

(3) Since Cathy invested $\frac{6000}{12000}$ of the money, how much of the amount calculated in (2) should she get if profit is distributed in proportion to investment?

Answer 2

profit = 40 percent of the total investment = $ (40 /100) *(2400 + 3600 + 6000) = 4800$

tax = 30 percent of profit = $ (30 /100) *(4800) = 1440$

left out money after taxing = profit - tax = $ 4800 - 1440 = 3360 $

chatty share = $ (5/10) * 3360 = 1680 $ (because profit divided in same ratio as investment 24:36:60 which is 2 : 3 :5)

Answer is $1680

Answer 3

Or, moving the messy calculations to the end:

Everyone made $40\%$ profit; they were allowed to keep $70\%$ of the $40\%$, or a $28\%$ profit.

Find $28\%$ of $\$2400$, $28\%$ of $\$3600$, and $28\%$ of $\$6000$