Two partners invest X 125000 and X 85000, respectively in a business and agree that 60% of the profit should be divided equally between them and the remaining profit is to be treated as interest on capital. If one partner gets X 600 more than the other, find the total profit made in the business.

Options

A. X 8800
B. X 8885
C. X 8995
D. X 7875

Answer

To solve the problem step by step, we will first define the variables and then calculate the total profit made in the business based on the given conditions.

### Step 1: Define the investments and profit sharing
Let Partner A invest \( X_A = 125,000 \) and Partner B invest \( X_B = 85,000 \).

### Step 2: Calculate the total investment
The total investment in the business is:
\[ X_A + X_B = 125,000 + 85,000 = 210,000 \]

### Step 3: Define the total profit
Let the total profit be \( P \).

### Step 4: Calculate the share of profit to be divided equally
According to the problem, 60% of the profit is to be divided equally between the two partners. Therefore, the amount to be divided equally is:
\[ 0.6P \]
Each partner will receive:
\[ \text{Equal share for each} = \frac{0.6P}{2} = 0.3P \]

### Step 5: Calculate the remaining profit
The remaining profit, which is treated as interest on capital, is:
\[ 0.4P \]

### Step 6: Calculate the ratio of interest on capital
The ratio of their investments is:
\[ \text{Ratio} = \frac{X_A}{X_B} = \frac{125,000}{85,000} = \frac{125}{85} = \frac{25}{17} \]
This means for every 25 parts of interest, Partner A gets 25 parts and Partner B gets 17 parts.

### Step 7: Calculate the total parts for interest distribution
The total parts for interest distribution is:
\[ 25 + 17 = 42 \]

### Step 8: Calculate the shares of interest for each partner
The share of interest for Partner A:
\[ \text{Interest share for A} = \frac{25}{42} \times 0.4P = \frac{10P}{42} = \frac{5P}{21} \]
The share of interest for Partner B:
\[ \text{Interest share for B} = \frac{17}{42} \times 0.4P = \frac{6.8P}{42} = \frac{34P}{210} = \frac{17P}{105} \]

### Step 9: Calculate total earnings for each partner
Total earnings for Partner A:
\[ \text{Total earnings for A} = 0.3P + \frac{5P}{21} \]
Total earnings for Partner B:
\[ \text{Total earnings for B} = 0.3P + \frac{17P}{105} \]

### Step 10: Set up the equation based on the difference in earnings
According to the problem, Partner A earns \( 600 \) more than Partner B:
\[ \left(0.3P + \frac{5P}{21}\right) - \left(0.3P + \frac{17P}{105}\right) = 600 \]
This simplifies to:
\[ \frac{5P}{21} - \frac{17P}{105} = 600 \]

### Step 11: Find a common denominator and solve for \( P \)
The common denominator for \( 21 \) and \( 105 \) is \( 105 \):
\[ \frac{25P}{105} - \frac{17P}{105} = 600 \]
\[ \frac{8P}{105} = 600 \]
Multiplying both sides by \( 105 \):
\[ 8P = 63000 \]
Dividing both sides by \( 8 \):
\[ P = 7875 \]

### Final Answer
The total profit made in the business is \( \text{X} 7875 \).