Three partners A,B and c invested their amounts in ratio of `3:5:7` . At the end of four months . A invests some amount such that , his total investment will be equal to C's initial investment .If C's share in profit is Rs 3150 then what will be total annual profit ?

Options

A. A)Rs 8150
B. B)Rs 7950
C. C)Rs 8000
D. D)Rs 7500

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the Initial Investment Ratios
The initial investment ratios of partners A, B, and C are given as:
- A : B : C = 3 : 5 : 7

### Step 2: Calculate the Effective Investment for the First 4 Months
Since the investments are made for 4 months, we can calculate the effective investment for each partner for this period:
- A's effective investment for 4 months = \( 3 \times 4 = 12 \)
- B's effective investment for 4 months = \( 5 \times 4 = 20 \)
- C's effective investment for 4 months = \( 7 \times 4 = 28 \)

### Step 3: A's Additional Investment
After 4 months, A invests an additional amount so that his total investment equals C's initial investment (which is 7). Therefore, A's new investment becomes:
- A's new investment = \( 3 + 4 = 7 \)

### Step 4: Calculate Effective Investment for the Remaining 8 Months
Now, we calculate the effective investment for the remaining 8 months:
- A's effective investment for the next 8 months = \( 7 \times 8 = 56 \)
- B's effective investment for the next 8 months = \( 5 \times 8 = 40 \)
- C's effective investment for the next 8 months = \( 7 \times 8 = 56 \)

### Step 5: Calculate Total Effective Investment
Now we can calculate the total effective investment for each partner:
- Total effective investment for A = \( 12 + 56 = 68 \)
- Total effective investment for B = \( 20 + 40 = 60 \)
- Total effective investment for C = \( 28 + 56 = 84 \)

### Step 6: Determine the Profit Ratio
The profit ratio based on the total effective investments is:
- A : B : C = 68 : 60 : 84

### Step 7: Simplify the Profit Ratio
To simplify the ratio, we can divide each term by 4:
- A : B : C = \( 17 : 15 : 21 \)

### Step 8: Relate C's Profit to the Ratio
We know that C's share in profit is Rs 3150, which corresponds to 21 parts of the profit ratio. Therefore, we can set up the equation:
- \( 21 \text{ units} = 3150 \)

### Step 9: Calculate the Value of One Unit
To find the value of one unit, we divide C's profit by the number of units:
- Value of 1 unit = \( \frac{3150}{21} = 150 \)

### Step 10: Calculate Total Profit
Now, we can calculate the total profit using the total number of units from the profit ratio:
- Total units = \( 17 + 15 + 21 = 53 \)
- Total profit = \( 53 \times 150 = 7950 \)

### Final Answer
The total annual profit is Rs 7950.

---