A and B started a business with X 20000 and X 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 X 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 determine how the premium paid by C will be divided between A and B based on their initial investments and the new profit-sharing agreement.

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

### Step 2: Calculate the ratio of A's and B's capital contributions.
- The ratio of A's capital to B's capital = 20,000 : 35,000
- Simplifying this ratio:
\[ \text{Ratio} = \frac{20,000}{5,000} : \frac{35,000}{5,000} = 4 : 7 \]

### Step 3: Calculate the total profit-sharing ratio before C joins.
- Before C joins, A and B share profits in the ratio of their capitals, which is 4:7.

### Step 4: Determine the premium paid by C.
- C pays a premium of ₹220,000 to join the partnership.

### Step 5: Determine how the premium will be shared between A and B.
- Since A and B will now share profits equally with C, we need to divide the premium in the ratio of their initial capital contributions (4:7).

### Step 6: Calculate the total parts in the ratio.
- Total parts = 4 + 7 = 11 parts.

### Step 7: Calculate A's share of the premium.
- A's share of the premium = \(\frac{4}{11} \times 220,000\)
\[ = \frac{880,000}{11} = ₹80,000 \]

### Step 8: Calculate B's share of the premium.
- B's share of the premium = \(\frac{7}{11} \times 220,000\)
\[ = \frac{1,540,000}{11} = ₹140,000 \]

### Step 9: State the final shares of A and B.
- A receives ₹80,000 from the premium.
- B receives ₹140,000 from the premium.

### Final Answer:
The premium of ₹220,000 paid by C will be divided between A and B in the ratio of 4:7, where A receives ₹80,000 and B receives ₹140,000.

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