A, B and C enter into a partanership by investing Rs. 3600, Rs. 4400. and Rs,2800. A is a working partner and gets a fourth of the profit for his service and the remaining profit is divided amongst the three in the rate of their investments. What is the amount of profit that B gets if A gets a total of Rs. `8000`?

Options

A. `4888.88`
B. `9333.33`
C. `4.0`
D. `3666.66`

Answer

To solve the problem step by step, we need to follow these calculations:

### Step 1: Determine the total profit
Let the total profit be denoted as \( X \). We know that A receives a fourth of the total profit for his service, and the remaining profit is divided among A, B, and C based on their investments.

### Step 2: Calculate A's share of the profit
A's share from the profit is given as:
\[ \text{A's share} = \frac{1}{4} X \]
According to the problem, A's total amount received is Rs. 8000. Therefore, we can set up the equation:
\[ \frac{1}{4} X = 8000 \]

### Step 3: Solve for \( X \)
To find \( X \), we multiply both sides of the equation by 4:
\[ X = 8000 \times 4 = 32000 \]

### Step 4: Calculate the remaining profit
The remaining profit after A's share is:
\[ \text{Remaining profit} = X - \frac{1}{4} X = \frac{3}{4} X \]
Substituting the value of \( X \):
\[ \text{Remaining profit} = \frac{3}{4} \times 32000 = 24000 \]

### Step 5: Determine the ratio of investments
The investments of A, B, and C are Rs. 3600, Rs. 4400, and Rs. 2800 respectively. We first find the total investment:
\[ \text{Total investment} = 3600 + 4400 + 2800 = 10800 \]
Now, we can find the ratio of their investments:
- A's investment ratio: \( \frac{3600}{10800} = \frac{1}{3} \)
- B's investment ratio: \( \frac{4400}{10800} = \frac{11}{27} \)
- C's investment ratio: \( \frac{2800}{10800} = \frac{7}{27} \)

### Step 6: Calculate B's share of the remaining profit
B's share of the remaining profit is calculated by multiplying the remaining profit by B's investment ratio:
\[ \text{B's share} = \frac{11}{27} \times 24000 \]
Calculating this gives:
\[ \text{B's share} = \frac{11 \times 24000}{27} = \frac{264000}{27} \approx 9777.78 \]

### Final Answer
Thus, the amount of profit that B gets is approximately Rs. 9777.78.

---