A,B & C entered into a partnership business with capital in the ratio `5:8:12` .After 8 months C withdraws his capital while after 10 months B increased his investment by 25 % . If at the end of the year difference between profit share of A and B is Rs . 17000, then find profit share of C at the end of the year .

Options

A. A)Rs 40800
B. B)Rs 46200
C. C)Rs 32400
D. D)Rs 50400

Answer

To solve the problem step by step, we will follow the details provided in the question and the video transcript.

### Step 1: Determine the initial capital contributions
The capital contributions of A, B, and C are in the ratio of 5:8:12. Let's denote their investments as:
- A's investment = 5x
- B's investment = 8x
- C's investment = 12x

### Step 2: Calculate the effective capital for each partner
- A invests for 12 months.
- B invests for 12 months but increases his investment after 10 months.
- C invests for 8 months and then withdraws his capital.

**Calculating the effective capital:**
- A's effective capital = 5x * 12 = 60x
- B's effective capital for the first 10 months = 8x * 10 = 80x
- B's increased investment after 10 months = 25% of 8x = 2x, so new investment = 8x + 2x = 10x.
- B's effective capital for the last 2 months = 10x * 2 = 20x
- Total effective capital for B = 80x + 20x = 100x
- C's effective capital = 12x * 8 = 96x (since he withdraws after 8 months)

### Step 3: Calculate total effective capital
Now we have:
- A's effective capital = 60x
- B's effective capital = 100x
- C's effective capital = 96x

### Step 4: Calculate the total effective capital
Total effective capital = A's effective capital + B's effective capital + C's effective capital
= 60x + 100x + 96x = 256x

### Step 5: Determine the profit-sharing ratio
The profit-sharing ratio will be based on their effective capitals:
- A's share = 60x
- B's share = 100x
- C's share = 96x

The profit-sharing ratio of A : B : C = 60 : 100 : 96.

### Step 6: Simplify the profit-sharing ratio
To simplify the ratio, we can divide each term by 4:
- A : B : C = 15 : 25 : 24.

### Step 7: Use the given difference in profit to find the profit share of C
According to the problem, the difference between the profit shares of A and B is Rs. 17,000.

The difference in their shares can be calculated as:
- Difference = B's share - A's share = (25 - 15) units = 10 units.

### Step 8: Calculate the value of one unit
If 10 units = Rs. 17,000, then:
- 1 unit = Rs. 17,000 / 10 = Rs. 1,700.

### Step 9: Calculate C's profit share
C's share in the profit is represented by 24 units. Therefore, C's profit share = 24 units * Rs. 1,700/unit = Rs. 40,800.

### Final Answer
C's profit share at the end of the year is Rs. 40,800.

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