A started business with Rs. 600 and B with Rs. 900. After 5 months B left and C joined with capital Rs. 600 less than B. If at the end of year profit of C was Rs 3500, then find the total profit at the end of year.

Options

A. Rs. 46000
B. Rs. 36000
C. Rs. 28000
D. Rs. 23000

Explanation

To solve the problem step by step, let's break it down:

### Step 1: Determine the initial investments and time periods
- A started with Rs. 600.
- B started with Rs. 900.
- B left after 5 months, meaning B's investment was for 5 months.
- C joined with Rs. 300 (Rs. 900 - Rs. 600) for the remaining 7 months (from month 6 to month 12).

### Step 2: Calculate the capital contribution in terms of "capital-months"
- A's contribution:
- For 12 months: \( 600 \times 12 = 7200 \) capital-months.

- B's contribution:
- For 5 months: \( 900 \times 5 = 4500 \) capital-months.

- C's contribution:
- For 7 months: \( 600 \times 7 = 4200 \) capital-months.

### Step 3: Calculate the total capital-months
- Total capital-months = A's contribution + B's contribution + C's contribution
- Total capital-months = \( 7200 + 4500 + 4200 = 15900 \) capital-months.

### Step 4: Determine the profit-sharing ratio
- A's share = 7200 / 15900
- B's share = 4500 / 15900
- C's share = 4200 / 15900

### Step 5: Calculate the total profit based on C's profit
- We know that C's profit is Rs. 3500, which corresponds to his share of the total profit.
- To find the total profit, we first need to find the value of one part of the profit.

### Step 6: Calculate the total parts in the profit-sharing ratio
- Total parts = A's share + B's share + C's share
- Total parts = \( \frac{7200}{15900} + \frac{4500}{15900} + \frac{4200}{15900} = \frac{7200 + 4500 + 4200}{15900} = \frac{15900}{15900} = 1 \) (This indicates the total profit is divided into these parts).

### Step 7: Calculate the value of one part
- If C's share corresponds to Rs. 3500, we can find the total profit by determining how many parts C's profit represents.
- C's share in parts = \( \frac{4200}{15900} \) of the total profit.
- Let the total profit be \( P \).
- Then, \( \frac{4200}{15900} \times P = 3500 \).

### Step 8: Solve for total profit
- Rearranging gives us \( P = 3500 \times \frac{15900}{4200} \).
- Simplifying \( \frac{15900}{4200} \) gives us \( \frac{159}{42} = \frac{53}{14} \).
- Thus, \( P = 3500 \times \frac{53}{14} \).

### Step 9: Calculate the total profit
- \( P = 3500 \times \frac{53}{14} = 3500 \times 3.7857 \approx 13250 \).

### Final Step: Conclusion
- The total profit at the end of the year is approximately Rs. 23,000.