A and B started a business after investing Rs. 12,000 and Rs. 14,400 respectively. At the end of the year B gets 12% of the total profit as management fees and the rest amount is distributed between both the partners in the ratio of their investments. If total annual profit is Rs. 7,500, then find the difference between their profits.

Options

A. A) Rs. 1250
B. B) Rs. 600
C. C) Rs. 900
D. D) Rs. 1500

Answer

To solve the problem step by step, we will follow the given information and perform the necessary calculations.

### Step 1: Calculate B's Management Fees
B receives 12% of the total profit as management fees. The total profit is Rs. 7,500.

\[ \text{Management Fees} = 12\% \text{ of } 7500 = \frac{12}{100} \times 7500 = 900 \text{ Rs.} \]

### Step 2: Calculate the Remaining Profit
After paying B's management fees, we need to find the remaining profit that will be distributed between A and B.

\[ \text{Remaining Profit} = \text{Total Profit} - \text{Management Fees} = 7500 - 900 = 6600 \text{ Rs.} \]

### Step 3: Determine the Investment Ratio
A and B invested Rs. 12,000 and Rs. 14,400 respectively. We need to find the ratio of their investments.

\[ \text{Investment Ratio of A to B} = \frac{12000}{14400} = \frac{5}{6} \]

### Step 4: Calculate A's and B's Share of the Remaining Profit
The remaining profit of Rs. 6600 will be distributed according to their investment ratio (5:6).

- Total parts = 5 + 6 = 11 parts

A's share:
\[ \text{A's Share} = \frac{5}{11} \times 6600 = 3000 \text{ Rs.} \]

B's share:
\[ \text{B's Share} = \frac{6}{11} \times 6600 = 3600 \text{ Rs.} \]

### Step 5: Calculate Total Profit for A and B
Now, we need to calculate the total profit for both A and B.

- Total profit for A:
\[ \text{Total Profit for A} = \text{A's Share} = 3000 \text{ Rs.} \]

- Total profit for B:
\[ \text{Total Profit for B} = \text{B's Share} + \text{Management Fees} = 3600 + 900 = 4500 \text{ Rs.} \]

### Step 6: Find the Difference Between Their Profits
Finally, we need to find the difference between A's and B's total profits.

\[ \text{Difference} = \text{Total Profit for B} - \text{Total Profit for A} = 4500 - 3000 = 1500 \text{ Rs.} \]

### Final Answer
The difference between their profits is Rs. 1500.

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