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Question 1088873: Alex and Jimmy entered into a business partnership in 1985.the total capital of the business was $27,000 which they agreed to contribute in the ratio 2:1 respectively. the annual profit was shared as follows: Alex was paid 5.5% of the total profit for his service as a manager. The remainder of the profit was shared in the ratio of their contributions to the capital. if Alex received $6,850 out of the total profit.
1. what is the total profit of the year
2. calculate Jimmy's share of the profit as a percentage of his initial contribution to the capital.
3. if Alex had to pay 30% of the amount he received as tax, how much did he pay??
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the total amount invested = 27,000
alex contributed 2 times the amount that jimmy contributed.
alex contributed 2/3 * 27,000 = 18,000.
jimmy contributed 1/3 * 27,000 = 9,000.
the annual profit was shared as follows:
alex was paid 5.5% of the total profit for his service as a manager.
the remainder of the profit was shared in the ratio of their respective contributions.
alex receives 6850 of the total profit.
this includes his share from his contribution to the total capital plus the amount he received from being a service manager.
let x equal the total profit.
alex take .055 * x for himself.
the rest of the profit is equal to (1 - .055) * x which is equal to .945 * x
this is divided between them in the ratio of 2 parts for alex and 1 part for jimmy.
2 parts plus 1 part = 3 parts.
alex gets 2/3 of the remaiinng profit and jimmy gets 1/3 of the remaining profit.
alex gets 2/3 * .945 * x = .63 * x.
jimmy gets 1/3 * .945 * x = .315 * x.
the total that alex gets is .63 * x + .055 * x
that's his share of the remaining profit plus his service manager fee.
this is equal to 6850.
your equation is 6850 = .63 * x + .055 * x
combine like terms to get 6850 = .685 * x
solve for x to get x = 6850 / .685 = 10,000
that's the total profit for the year.
to confirm:
total profit for the year is 10,000
alex gets 5.5% of this which is equal to 550.
the remainder is 10,000 minus 550 = 9,450
9,450 is divided between alex and jimmy in the ratio of 2 parts for alex and 1 part for jimmy.
since alex gets 2 parts and jimmy gets 1 part, then the total number of parts must be equal to 3.
divide 9450 by 3 to get 1 part = 3150.
2 parts is therefore equal to 6300.
total alex gets is 6300 + 550 = 6850.
jimmy gets 3150.
6850 + 3150 = 10,000
formula checks out.
solution is assumed to be good.
the questions with their solutions are shown below:
1. what is the total profit of the year
total profit of the year is 10,000
2. calculate Jimmy's share of the profit as a percentage of his initial contribution to the capital.
jimmy's share of the profit is 3150.
jimmy's initial contribution to the capital is 9,000.
jimmy's share of the profit as a percentage of his initial contribution to the capital is 3150 / 9000 = .35 = 35%
3. if Alex had to pay 30% of the amount he received as tax, how much did he pay??
alex' share of the profit is 6850.
if he had to pay 30% tax on this, then he had to pay .30 * 6850 = 2055 tax.
i believe that answers your question.
let me know if you have any further questions regarding it.
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