A and B started a business , Investment of A was 899 rs. After 8 months from start of business B left and C joined with amount double of that of B. if A's share out of total annual profit of 14005 rs was 5039.5rs. What was C's approximate investment

Options

A. 3000
B. 1600
C. 1200
D. 2400

Answer

To solve the problem step by step, we will break down the information given and calculate C's investment based on the profits shared among A, B, and C.

### Step 1: Understand the Investments
- A's investment = Rs. 899
- Let B's investment = Rs. X
- Therefore, C's investment = 2X (since C invests double the amount of B)

### Step 2: Calculate A's Total Investment Over Time
- A's investment is for 12 months, so:
\[ \text{A's total investment} = 899 \times 12 = 10788 \text{ Rs.} \]

### Step 3: Calculate B's Investment Duration
- B invested for 8 months, so:
\[ \text{B's total investment} = X \times 8 = 8X \]

### Step 4: Calculate C's Investment Duration
- C joined after 8 months and invested for 4 months, so:
\[ \text{C's total investment} = 2X \times 4 = 8X \]

### Step 5: Total Investment Calculation
- Total investment by A, B, and C:
\[ \text{Total Investment} = \text{A's investment} + \text{B's investment} + \text{C's investment} \]
\[ = 10788 + 8X + 8X = 10788 + 16X \]

### Step 6: Profit Sharing
- Total profit = Rs. 14005
- A's share of profit = Rs. 5039.5
- The share of profit is proportional to the total investment:
\[ \frac{\text{A's share}}{\text{Total profit}} = \frac{\text{A's investment}}{\text{Total investment}} \]
\[ \frac{5039.5}{14005} = \frac{10788}{10788 + 16X} \]

### Step 7: Cross-Multiplying to Solve for X
Cross-multiplying gives us:
\[ 5039.5 \times (10788 + 16X) = 14005 \times 10788 \]
Expanding both sides:
\[ 5039.5 \times 10788 + 5039.5 \times 16X = 14005 \times 10788 \]
Calculating the left side:
\[ 54354666 + 5039.5 \times 16X = 150000840 \]
Now, isolate the term with X:
\[ 5039.5 \times 16X = 150000840 - 54354666 \]
Calculating the right side:
\[ 5039.5 \times 16X = 95646174 \]

### Step 8: Solve for X
Now divide both sides by 5039.5:
\[ 16X = \frac{95646174}{5039.5} \]
Calculating:
\[ 16X \approx 18900 \]
Now divide by 16:
\[ X \approx \frac{18900}{16} \approx 1181.25 \]

### Step 9: Calculate C's Investment
Since C's investment is double that of B:
\[ C's investment = 2X \approx 2 \times 1181.25 \approx 2362.5 \]

### Final Answer
C's approximate investment is Rs. 2362.5.