A and B started a business with Rs. 20000 and Rs. 35000 respectively. They agreed to share the profit in the ratio of their capital. C joins the partnership with the condition that A, B and C will share profit equally and pays Rs. 220000 as premium for this, to be shared between A and B. This is to be divided between A and B in the ratio of

Options

A. `10 : 1`
B. `1 : 10`
C. `9 : 10`
D. `10 : 9`

Answer

To solve the problem step by step, we need to analyze the contributions of A, B, and C to the business and how the profits will be shared.

### Step 1: Determine the initial capital contributions of A and B.
- A's capital = Rs. 20,000
- B's capital = Rs. 35,000

### Step 2: Calculate the total capital contributed by A and B.
Total capital = A's capital + B's capital
Total capital = 20,000 + 35,000 = Rs. 55,000

### Step 3: Determine the profit-sharing ratio of A and B based on their capital contributions.
- A's share of the capital = 20,000 / 55,000
- B's share of the capital = 35,000 / 55,000

To express this as a ratio, we can simplify:
- A's ratio = 20,000 : 55,000 = 20 : 55 = 4 : 11
- B's ratio = 35,000 : 55,000 = 35 : 55 = 7 : 11

Thus, the profit-sharing ratio of A and B based on their capital is 4:7.

### Step 4: C joins the partnership and pays a premium of Rs. 220,000.
C pays Rs. 220,000 to A and B for sharing profits equally.

### Step 5: Determine how the premium will be divided between A and B.
Since A and B will now share the premium based on their original capital ratio (4:7), we need to calculate their respective shares from the premium.

Total parts = 4 + 7 = 11 parts

- A's share of the premium = (4/11) * 220,000
- B's share of the premium = (7/11) * 220,000

Calculating A's share:
A's share = (4/11) * 220,000 = Rs. 80,000

Calculating B's share:
B's share = (7/11) * 220,000 = Rs. 140,000

### Step 6: Write the final ratio of A and B's shares of the premium.
The final ratio of A's share to B's share of the premium is:
A : B = 80,000 : 140,000 = 8 : 14 = 4 : 7

### Conclusion
Thus, the premium paid by C is divided between A and B in the ratio of 4:7.

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