B is a sleeping partner and A working. A puts in Rs 5,000 and B puts in 6,000. A received `12(1)/(2)%` of profit for managing the business and rest is divided in propoftion to their capitals. A's share of profit in a profit of Rs 880 is

Answer

To find A's share of the profit in a total profit of Rs. 880, we will follow these steps:

### Step 1: Identify the investments of A and B
- A's investment = Rs. 5000
- B's investment = Rs. 6000

### Step 2: Calculate the total profit
- Total profit = Rs. 880

### Step 3: Calculate A's share for managing the business
- A receives 12.5% of the total profit for managing the business.
- Convert 12.5% to a fraction:
\[ 12.5\% = \frac{12.5}{100} = \frac{1}{8} \]
- Calculate A's share for managing:
\[ A's\ share = \frac{1}{8} \times 880 = 110 \]

### Step 4: Calculate the remaining profit
- Remaining profit after A's share for managing:
\[ Remaining\ profit = Total\ profit - A's\ share = 880 - 110 = 770 \]

### Step 5: Calculate the ratio of their investments
- The ratio of A's investment to B's investment:
\[ A : B = 5000 : 6000 = 5 : 6 \]

### Step 6: Calculate A's share of the remaining profit
- Total parts in the ratio = 5 + 6 = 11
- A's share of the remaining profit:
\[ A's\ share = \frac{5}{11} \times 770 \]
- Calculate A's share:
\[ A's\ share = \frac{5 \times 770}{11} = \frac{3850}{11} = 350 \]

### Step 7: Calculate total profit share of A
- Total profit share of A:
\[ Total\ profit\ of\ A = A's\ share\ for\ managing + A's\ share\ of\ remaining\ profit \]
\[ Total\ profit\ of\ A = 110 + 350 = 460 \]

### Final Answer
- A's share of profit = Rs. 460

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