A and B jointly invest 2100 and 3100 respectively in a firm. A is an active partner and he gets 25% of the profit separately. If their business yields them total 1040 as profit, what will be the gain of each of them?

Options

A. 415, 3625
B. 575, 465
C. 515, 525
D. 560, 480

Answer

To solve the problem step by step, we will follow the outlined process:

### Step 1: Calculate A's Share of the Profit
A is an active partner and receives 25% of the total profit. The total profit is given as 1040.

\[ \text{A's share} = 25\% \text{ of } 1040 = \frac{25}{100} \times 1040 = 260 \]

### Step 2: Calculate the Remaining Profit
After giving A his share, we need to find the remaining profit that will be shared between A and B.

\[ \text{Remaining profit} = \text{Total profit} - \text{A's share} = 1040 - 260 = 780 \]

### Step 3: Calculate the Total Investment
Next, we need to find the total investment made by A and B.

\[ \text{Total investment} = A's investment + B's investment = 2100 + 3100 = 5200 \]

### Step 4: Calculate the Profit Sharing Ratio
Now we will determine the ratio of A's and B's investments to find out how the remaining profit will be divided.

\[ \text{A's investment} = 2100, \quad \text{B's investment} = 3100 \]
\[ \text{Ratio of A to B} = \frac{2100}{3100} = \frac{21}{31} \]

### Step 5: Calculate B's Share of the Remaining Profit
Now we will calculate B's share of the remaining profit based on the investment ratio.

\[ \text{Total parts} = 21 + 31 = 52 \]
\[ \text{B's share of remaining profit} = \frac{31}{52} \times 780 \]

Calculating B's share:

\[ \text{B's share} = \frac{31 \times 780}{52} = 31 \times 15 = 465 \]

### Step 6: Calculate A's Share of the Remaining Profit
Now we can find A's share of the remaining profit.

\[ \text{A's share of remaining profit} = \text{Remaining profit} - \text{B's share} = 780 - 465 = 315 \]

### Step 7: Calculate Total Gain of A and B
Finally, we will calculate the total gain for A and B.

\[ \text{Total gain of A} = \text{A's share} + \text{A's share of remaining profit} = 260 + 315 = 575 \]
\[ \text{Total gain of B} = \text{B's share} = 465 \]

### Final Answer
- A's total gain = 575
- B's total gain = 465