A, B and C entered into a partnership. A invested 2,560 and B 2,000. At the end of the year, they gained 1,105, out of which A got 320. C's capital was

Options

A. 4280
B. 2840
C. 4820
D. 4028

Answer

To find C's capital in the partnership, we can follow these steps:

### Step 1: Determine the total profit and A's share
The total profit from the partnership is given as 1,105. A's share of the profit is given as 320.

### Step 2: Calculate the profit share ratio
To find the profit share ratio, we first need to determine the total capital invested by A and B, and then find out how much of the profit C would have received.

- A's investment = 2,560
- B's investment = 2,000

Let C's investment be denoted as \( C \).

### Step 3: Calculate the total investment
The total investment by A, B, and C can be represented as:
\[ \text{Total Investment} = A + B + C = 2,560 + 2,000 + C \]

### Step 4: Determine the profit share for A and B
The profit share is distributed according to the amount invested. Therefore, we can set up the ratio of their investments:
- A's share of the total investment = \( \frac{2560}{2560 + 2000 + C} \)
- B's share of the total investment = \( \frac{2000}{2560 + 2000 + C} \)
- C's share of the total investment = \( \frac{C}{2560 + 2000 + C} \)

### Step 5: Set up the equation for A's profit
Since A received 320 out of the total profit of 1,105, we can set up the equation:
\[ 320 = \frac{2560}{2560 + 2000 + C} \times 1105 \]

### Step 6: Solve for C
1. Rearranging the equation:
\[ 320(2560 + 2000 + C) = 2560 \times 1105 \]
2. Expanding and simplifying:
\[ 320(4560 + C) = 2560 \times 1105 \]
3. Calculate \( 2560 \times 1105 \):
\[ 2560 \times 1105 = 2,826,800 \]
4. Substitute back into the equation:
\[ 320(4560 + C) = 2826800 \]
5. Divide both sides by 320:
\[ 4560 + C = \frac{2826800}{320} \]
6. Calculate \( \frac{2826800}{320} \):
\[ 4560 + C = 8821.25 \]
7. Finally, solve for C:
\[ C = 8821.25 - 4560 \]
\[ C = 4261.25 \]

### Conclusion
C's capital was approximately 4,261.25.