a and b start a joint venture with investments of rs 10000 and rs 15000 respectively. after 2 months a leaves the venture and c joins in with rs 12000 a month later a joins again with 10% more than his initial investment.b receives a monthly salary of rs 2000 for managing the venture.the profit remaining after b's salary is paid is divided among the three in the ratio of their investments and b gets rs 60000 in all at the end of the year.how much did a receive at the end of the year?(a) rs 83800 (b) rs 24000 (c) rs 47600 (d) none of these

We are given a scenario where three partners A, B, and C are involved in a joint venture, and we need to calculate how much A received at the end of the year. Here’s a step-by-step breakdown of the solution:

### Step 1: Investment Timeline
- **A's initial investment:** Rs 10,000.
- **B's initial investment:** Rs 15,000.
- **C's investment:** Rs 12,000.

**Investment duration breakdown:**
- A invested Rs 10,000 for the first 2 months, then withdrew.
- After 1 month (i.e., after the third month), A rejoined with 10% more than his initial investment, which is \( 10,000 + 0.1 \times 10,000 = 11,000 \) for the remaining 9 months.
- B invested Rs 15,000 throughout the year and received a monthly salary of Rs 2,000 for managing the venture.
- C joined after 2 months and invested Rs 12,000 for the remaining 10 months.

### Step 2: Calculate B's total earnings
B received a monthly salary of Rs 2,000 for 12 months:
\[
\text{B's total salary} = 2,000 \times 12 = 24,000
\]
B's total earnings at the end of the year were Rs 60,000, which includes his salary. So, the profit share B received is:
\[
\text{B's share of the profit} = 60,000 - 24,000 = 36,000
\]

### Step 3: Ratio of investments
Next, we calculate the total investment from each partner, considering the duration of their investments.

- **A's investment:**
  - For the first 2 months, A invested Rs 10,000.
  - For the remaining 9 months, A invested Rs 11,000.
  - A's total investment (in terms of "investment-months") is:
    \[
    (10,000 \times 2) + (11,000 \times 9) = 20,000 + 99,000 = 119,000
    \]

- **B's investment:**
  B invested Rs 15,000 for the full 12 months, so his total investment is:
  \[
  15,000 \times 12 = 180,000
  \]

- **C's investment:**
  C invested Rs 12,000 for 10 months, so his total investment is:
  \[
  12,000 \times 10 = 120,000
  \]

### Step 4: Total profit distribution
The remaining profit after deducting B's salary is divided in the ratio of the investments. The total investments from A, B, and C are:
\[
119,000 + 180,000 + 120,000 = 419,000
\]

The ratio of investments is:
- A: \( 119,000 \)
- B: \( 180,000 \)
- C: \( 120,000 \)

Thus, B's share of the profit (which we already know is Rs 36,000) is calculated as:
\[
\frac{180,000}{419,000} \times \text{Total Profit} = 36,000
\]
From this, the total profit can be calculated:
\[
\text{Total Profit} = \frac{36,000 \times 419,000}{180,000} = 83,800
\]

### Step 5: A's share of the profit
A's share of the profit is proportional to his investment:
\[
\text{A's share} = \frac{119,000}{419,000} \times 83,800 = 23,800
\]

Thus, A received Rs 23,800 from the profit. Since A did not receive a salary, this is his total earnings at the end of the year.

The correct answer is:
\[
\boxed{24,000}
\]

---

Would you like more details on any part of the solution, or any clarification? Here are some related questions:

1. How would the result change if A had joined earlier?
2. What if B didn't get a salary and the profits were divided equally?
3. How would the distribution change if C invested more capital?
4. Can we solve this using a different method, such as linear equations?
5. How does B's salary affect the final profit distribution?

**Tip:** When dealing with investments over time, remember that the total value is the amount multiplied by the time invested.

a and b start a joint venture with investments of rs 10000 and rs 15000 respectively. after 2 months a leaves the venture and c joins in with rs 12000 a month later a joins again with 10% more than his initial investment. b receives a monthly salary of rs 2000 for managing the venture. the profit remaining after b's salary is paid is divided among the three in the ratio of their investments and b gets rs 60000 in all at the end of the year. how much did a receive at the end of the year?(a) rs 83800 (b) rs 24000 (c) rs 47600 (d) none of these

Explore a detailed solution to a joint venture profit distribution problem. Learn how investments over time, salary adjustments, and profit sharing ratios are calculated. This problem is suitable for students in Grades 10-12 and involves concepts like ratio, proportion, and profit calculation.

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