SOLUTION: Three partners A,B and C agreed to share their annual net profit in the ratio 2 3 5. In a particular year they had to share 3/5 of the net profit and reinvest the rest in the busin

Question 1124202: Three partners A,B and C agreed to share their annual net profit in the ratio 2 3 5. In a particular year they had to share 3/5 of the net profit and reinvest the rest in the business. If A received 10000, how much did the other partners received?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the net profit is shared in the ratio of 2:3:5.

2 + 3 + 5 = 10.

A receives 2/10 of the profit.
B receives 3/10 of the profit.
C receives 5/10 of the profit.

the profit that they share is 3/5 of the total profit.

the rest of the profit (2/5) was reinvested in the business.

A receives 10,000 as his share of the profits that were available for sharing.

let x = the amount of the profits that were available for sharing.

then A's portion is 2/10 * x = 10,000.

solve for x to get x 10,000 * 10/2 = 50,000.

A gets 2/10 of 50,000 = 10,000.
B gets 3/10 of 50,000 = 15,000.
C gets 5/10 of 50,000 = 25,000

the ratio of A's share to B's share is 10,000 / 15,000 = 2/3
the ratio of B's share to C's share is 15,000 / 25,000 = 3/5

this can be shown as the ratio of A:B:C is 2:3:5.

this tells you that the ratio of A:B is 2:3, the ratio of B:C is 3:5, the ratio of A:C is 2:5.

since A gets 10,000 and B gets 15,000, the ratio of A:B is 10/15 = 2:3
since B gets 30,000 and C gets 25,000, the ratio of B:C is 30/50 = 3:5
since A gets 10,000 and C gets 25,000, the ratio of A:C is 10/25 = 2/5

now, 50,000 is the profit that was availble for sharin.

that represented 3/5 of the total profit.

if the total profit is x, then 50,000 = 3/5 * x.

solve for x to get x = 5/3 * 50,000 = 83,3333.33333...

your problem, however, did not ask for this.

it only asked for how much did the other partners receive.

you can do it by total as i did above, or you can do it by direct application of the ratios.

by total, the ratio of 2:3:5 yields a total of 10.

A receives 2/10 of the total hich is equal to 10,000.
the total has to be 50,000.
B receives 3/10 = 15,000
C receives 5/10 = 25,000

by direct application of the ratios, 2:3:5 means that B receives 3/2 * what A receives and C receives 5/3 * what B receives.

3/2 * 10,000 = 15,000
5/3 * 15,000 = 25,000

you can also work directly off of A, because C receives 5/2 * what A receives = 5/2 * 10,000 = 25,000.

the total method allows you to find how much profit was shared in total which allows you to find how much the total profit was, as i showed above.

here's a reference on ratios you might find helpful.

https://www.purplemath.com/modules/ratio.htm

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