A and B started a business in partnership with the investment of Rs.27000 and Rs .36000 respectively , after 4 months A withdraw 5000 Rs and B added 6000 Rs more and C joined with 35000 Rs . If after one year they gets a total profit of Rs . 130500, then find the profit share of C?

Options

A. A)36000 Rs
B. B)32000 Rs
C. C)35000 Rs
D. D)38000 Rs

Answer

To solve the problem step by step, we will calculate the profit share of C based on the investments made by A, B, and C over the year.

### Step 1: Calculate A's Contribution
A initially invested Rs. 27,000 for 4 months. After 4 months, A withdrew Rs. 5,000, leaving A with Rs. 22,000 for the remaining 8 months.

- Contribution for the first 4 months:
\[ 27000 \times 4 = 108000 \]
- Contribution for the next 8 months:
\[ 22000 \times 8 = 176000 \]
- Total contribution by A:
\[ 108000 + 176000 = 284000 \]

### Step 2: Calculate B's Contribution
B initially invested Rs. 36,000 for 4 months. After 4 months, B added Rs. 6,000, making the total investment Rs. 42,000 for the remaining 8 months.

- Contribution for the first 4 months:
\[ 36000 \times 4 = 144000 \]
- Contribution for the next 8 months:
\[ 42000 \times 8 = 336000 \]
- Total contribution by B:
\[ 144000 + 336000 = 480000 \]

### Step 3: Calculate C's Contribution
C joined the partnership with an investment of Rs. 35,000 for the last 8 months.

- Contribution by C:
\[ 35000 \times 8 = 280000 \]

### Step 4: Calculate Total Contributions
Now, we will sum up the total contributions from A, B, and C.

- Total contributions:
\[ A + B + C = 284000 + 480000 + 280000 = 1048000 \]

### Step 5: Calculate the Profit Ratio
Next, we will find the ratio of their contributions.

- A's contribution in terms of "months":
\[ 284000 \text{ (A's total contribution)} \]
- B's contribution in terms of "months":
\[ 480000 \text{ (B's total contribution)} \]
- C's contribution in terms of "months":
\[ 280000 \text{ (C's total contribution)} \]

Now we can express the profit sharing ratio:
- A : B : C = 284 : 480 : 280

### Step 6: Simplify the Ratio
To simplify the ratio, we can divide each term by 4:
- A : B : C = 71 : 120 : 70

### Step 7: Calculate Total Parts
Now, we will find the total parts in the ratio:
\[ 71 + 120 + 70 = 261 \]

### Step 8: Calculate the Value of Each Part
The total profit is Rs. 130,500. We will find the value of each part:
\[ \text{Value of 1 part} = \frac{130500}{261} = 500 \]

### Step 9: Calculate C's Profit Share
Now, we can calculate C's profit share:
\[ \text{C's profit share} = 70 \times 500 = 35000 \]

### Final Answer
C's profit share is Rs. 35,000.

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