A and B started a business by investing Rs20000 and Rs 25000, respectively. After 4 months B left and C joined by investing Rs15000. At the end of the year, there was a profit of Rs 23000. What is Cs share ?

Options

A. Rs8000
B. Rs9000
C. Rs6000
D. Rs12000

Answer

To find C's share of the profit, we will follow these steps:

### Step 1: Determine the investment and time for each partner
- A invested Rs. 20,000 for 12 months.
- B invested Rs. 25,000 for 4 months (since B left after 4 months).
- C invested Rs. 15,000 for 8 months (since C joined after B left).

### Step 2: Calculate the capital contribution of each partner
- A's contribution = Investment × Time = 20,000 × 12 = 240,000
- B's contribution = Investment × Time = 25,000 × 4 = 100,000
- C's contribution = Investment × Time = 15,000 × 8 = 120,000

### Step 3: Find the total contributions
Now, we will sum up the contributions:
- Total contributions = A's contribution + B's contribution + C's contribution
- Total contributions = 240,000 + 100,000 + 120,000 = 460,000

### Step 4: Determine the ratio of their contributions
The ratio of A, B, and C's contributions is:
- A : B : C = 240,000 : 100,000 : 120,000

To simplify this ratio, we can divide each term by 20,000:
- A : B : C = 12 : 5 : 6

### Step 5: Calculate the total parts in the profit
Now, we add the parts of the ratio:
- Total parts = 12 + 5 + 6 = 23 parts

### Step 6: Determine the value of each part
The total profit is Rs. 23,000. To find the value of one part:
- Value of one part = Total Profit / Total Parts = 23,000 / 23 = Rs. 1,000

### Step 7: Calculate C's share
C's share corresponds to 6 parts:
- C's share = Value of one part × C's parts = 1,000 × 6 = Rs. 6,000

### Final Answer
C's share of the profit is Rs. 6,000.

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