A, B and C invest in a business in the ratio 3 : 6 : 5. A and C are working partners. Only B is a sleeping partner hence his share will be 3/4th of what it would have been if he were a working partner. If they make Rs 50,000 profit, half of which is reinvested in the business and the other half is distributed between the partners, then how much does C get (in Rs)?

Options

A. 20000
B. 6000
C. 10000
D. 9000

Answer

To solve the problem step-by-step, we will follow these calculations:

### Step 1: Determine the initial investment ratio
The investment ratio of A, B, and C is given as 3:6:5.

### Step 2: Calculate the total parts of the investment
Total parts = 3 + 6 + 5 = 14 parts.

### Step 3: Calculate B's adjusted share
Since B is a sleeping partner, his share will be 3/4 of what it would have been if he were a working partner.
- If B were a working partner, his share would be 6 parts.
- Hence, B's actual share = (3/4) * 6 = 4.5 parts.

### Step 4: Update the investment ratio
Now, the new ratio of A, B, and C becomes:
- A = 3 parts
- B = 4.5 parts
- C = 5 parts

### Step 5: Convert the ratio to whole numbers
To eliminate the decimal, we can multiply the entire ratio by 2:
- A = 3 * 2 = 6 parts
- B = 4.5 * 2 = 9 parts
- C = 5 * 2 = 10 parts

Thus, the new ratio is 6:9:10.

### Step 6: Calculate the total parts in the new ratio
Total parts = 6 + 9 + 10 = 25 parts.

### Step 7: Calculate the total profit to be distributed
The total profit made is Rs 50,000. Half of this profit is reinvested, and the other half is distributed:
- Amount to be distributed = 50,000 / 2 = Rs 25,000.

### Step 8: Calculate C's share from the distributed profit
C's share in the profit distribution can be calculated using the ratio:
- C's share = (C's parts / Total parts) * Amount to be distributed
- C's share = (10 / 25) * 25,000 = 10,000.

### Final Answer
C receives Rs 10,000.

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