A B & C contributed #8000, #6000, #4000 respectively as capital to an enterprise. Out of the total profit, C received #500 for his services as manager. Each of them received 20% on their first #3000 of His capital & the remaining profit was shared in the ratio of the remaining parts of their capitals. If at the end of the year C received #1200 in total, find the total profit and amounts which A and B respectively received?
C received #500
Each of them received 20% on their first #3000
so, each got another #600
Then, if the remaining profit was x, then
A got 8/18 x
B got 6/18 x
C got 4/18 x = 1200 - 500 - 600 = 100
so, x = 450
Of that,
A got 200
B got 150
So the total amount for each was
A: 600+200 = 800
B: 600+150 = 750
C: 500+600+100 = 1200
To find the total profit and amounts received by A and B, we need to follow these steps:
1. Calculate the total capital contributed by A, B, and C.
- A contributed #8000
- B contributed #6000
- C contributed #4000
Total capital = #8000 + #6000 + #4000 = #18000
2. Calculate the total profit.
To find the total profit, we need to find the profit received by C for managing the enterprise and the remaining profit shared among A, B, and C.
- C received #500 for his services as manager.
- C received #1200 in total.
So, the remaining profit shared among A, B, and C can be calculated as follows:
Remaining profit = Total profit - Profit received by C for managing - Profit received by C in total
Remaining profit = Total profit - #500 - #1200
3. Calculate the profit received by A and B on the first #3000 of their capital.
Each of them received 20% on their first #3000 of their capital.
Profit received by A = 20% of #3000 = 0.2 * #3000 = #600
Profit received by B = 20% of #3000 = 0.2 * #3000 = #600
4. Calculate the remaining profit to be shared among A, B, and C in the ratio of their remaining capital.
Remaining profit to be shared among A, B, and C = Remaining profit - Profit received by A on the first #3000 - Profit received by B on the first #3000
Remaining profit to be shared among A, B, and C = Remaining profit - #600 - #600
5. Calculate the ratio of the remaining parts of their capital.
Ratio = Remaining capital of A : Remaining capital of B : Remaining capital of C
Ratio = (Total capital - #3000 - #3000) : (Total capital - #3000 - #3000) : (Total capital - #3000 - #3000)
Ratio = (#18000 - #3000 - #3000) : (#18000 - #3000 - #3000) : (#18000 - #3000 - #3000)
6. Calculate the amounts received by A and B in the ratio calculated in step 5.
Amount received by A = (Ratio of A / Sum of ratio) * Remaining profit to be shared
Amount received by B = (Ratio of B / Sum of ratio) * Remaining profit to be shared
Thus, by following these steps, we can find the total profit and amounts received by A and B.