Two persons A and B invested in a business with 115000and 75000 rupees respectively. They agree that 40% of theprofit should be divided equally among them and rest isdivided between them according to their investment. If Agot 500 rupee more than B, then the total profit is

Options

A. A) 3599.34
B. B) 699.34
C. C) 3958.34
D. D) 999.34

Answer

To solve the problem, we need to determine the total profit (P) based on the investments of A and B and the distribution of profit as described. Let's break it down step by step.

### Step 1: Understand the Investment
A invests ₹115,000 and B invests ₹75,000.

### Step 2: Calculate the Total Investment
Total investment = A's investment + B's investment
Total investment = ₹115,000 + ₹75,000 = ₹190,000

### Step 3: Determine the Profit Distribution
According to the problem, 40% of the profit (P) is divided equally between A and B, and the remaining 60% is divided according to their investments.

### Step 4: Calculate the Equal Share
Equal share from 40% of profit:
Each person’s equal share = 40% of P / 2
= (0.40 * P) / 2
= 0.20P

### Step 5: Calculate the Remaining Profit
Remaining profit to be divided according to investment = 60% of P
= 0.60P

### Step 6: Calculate A's and B's Share from the Remaining Profit
A's share from the remaining profit = (A's investment / Total investment) * Remaining profit
= (115,000 / 190,000) * (0.60P)
= (115/190) * 0.60P
= (115/190) * 0.60P = (69/114) * P

B's share from the remaining profit = (B's investment / Total investment) * Remaining profit
= (75,000 / 190,000) * (0.60P)
= (75/190) * 0.60P
= (75/190) * 0.60P = (45/114) * P

### Step 7: Calculate Total Earnings for A and B
Total earnings for A = Equal share + A's share from remaining profit
= 0.20P + (69/114) * P
= (0.20 + 69/114)P
= (0.20 + 0.6053)P
= (0.8053)P

Total earnings for B = Equal share + B's share from remaining profit
= 0.20P + (45/114) * P
= (0.20 + 45/114)P
= (0.20 + 0.3947)P
= (0.5947)P

### Step 8: Set Up the Equation
According to the problem, A earns ₹500 more than B:
(0.8053)P - (0.5947)P = 500
= 0.2106P = 500

### Step 9: Solve for P
P = 500 / 0.2106
P ≈ ₹2,373.59

### Step 10: Conclusion
The total profit (P) is approximately ₹2,373.59.

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