Two persons A and B invested in a business with 115000 and 75000 rupees respecitvely. They agree that `40%` of the profit should be divided equally among them and rest is divided btween them according to their investemnt. If A got 500 rupee more than B , then the total profit is.

Options

A. 3399.34
B. 699.34
C. 3958.34
D. 999.34

Explanation

To solve the problem step by step, we will break it down into manageable parts.

### Step 1: Define the Investments
Let the investment of A be \( A = 115000 \) rupees and the investment of B be \( B = 75000 \) rupees.

### Step 2: Calculate the Total Investment
The total investment \( T \) is given by:
\[ T = A + B = 115000 + 75000 = 190000 \text{ rupees} \]

### Step 3: Determine the Profit Sharing
According to the problem, 40% of the total profit \( P \) is shared equally between A and B. The remaining 60% is divided based on their investments.

### Step 4: Calculate Individual Shares from the Profit
Let’s denote the total profit as \( P \).

- The amount shared equally:
\[ \text{Equal share for A and B} = \frac{40}{100} \times P \div 2 = \frac{20}{100} \times P = 0.2P \]

- The remaining 60% of the profit is:
\[ \text{Remaining profit} = \frac{60}{100} \times P = 0.6P \]

### Step 5: Calculate the Ratio of Investments
The ratio of A's investment to B's investment is:
\[ \text{Ratio} = \frac{A}{B} = \frac{115000}{75000} = \frac{23}{15} \]

### Step 6: Calculate Individual Shares from the Remaining Profit
Now, we need to distribute the remaining profit (60%) according to their investment ratio:
- A's share from the remaining profit:
\[ \text{A's share from remaining profit} = \frac{23}{38} \times 0.6P \]
- B's share from the remaining profit:
\[ \text{B's share from remaining profit} = \frac{15}{38} \times 0.6P \]

### Step 7: Total Profit for A and B
Now, we can express the total profit for A and B:
- Total profit for A:
\[ \text{Total profit for A} = 0.2P + \frac{23}{38} \times 0.6P \]
- Total profit for B:
\[ \text{Total profit for B} = 0.2P + \frac{15}{38} \times 0.6P \]

### Step 8: Set Up the Equation
According to the problem, A got 500 rupees more than B:
\[ \text{Total profit for A} - \text{Total profit for B} = 500 \]

Substituting the expressions we derived:
\[ \left(0.2P + \frac{23}{38} \times 0.6P\right) - \left(0.2P + \frac{15}{38} \times 0.6P\right) = 500 \]

### Step 9: Simplify the Equation
This simplifies to:
\[ \frac{23}{38} \times 0.6P - \frac{15}{38} \times 0.6P = 500 \]
\[ \frac{(23 - 15)}{38} \times 0.6P = 500 \]
\[ \frac{8}{38} \times 0.6P = 500 \]

### Step 10: Solve for P
Now we can solve for \( P \):
\[ 0.6P = 500 \times \frac{38}{8} \]
\[ P = \frac{500 \times 38}{8 \times 0.6} \]
\[ P = \frac{19000}{4.8} = 3958.33 \text{ rupees} \]

### Final Answer
The total profit \( P \) is approximately \( 3958.34 \) rupees.

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