Question

Alex, Benn and Cole were partners in a firm sharing profits and losses in the ratio of 5:3:2. They admitted Dona as a new partner for \( \frac{1}{5} \) share in the future profits. Dona agreed to contribute proportionate capital. On the date of admission, capitals of Alex, Benn and Cole after all adjustments were Rs. 1,20,000; Rs. 80,000 and Rs. 1,00,000 respectively. The amount of capital brought in by Dona will be:

• A. Rs. 75,000
• B. Rs. 60,000
• C. Rs. 65,000
• D. Rs. 70,000

Hint:

When a new partner brings proportionate capital, first determine the total capital of old partners corresponding to their profit share, then calculate the total firm capital and finally find the new partner's share.

Answer 1

The Correct Option is A

Step 1: Determine total capital of existing partners.
Capital of Alex = Rs. 1,20,000
Capital of Benn = Rs. 80,000
Capital of Cole = Rs. 1,00,000
\[ \text{Total capital of old partners} = 1,20,000 + 80,000 + 1,00,000 = 3,00,000 \]
Step 2: Determine Dona's share in profits.
Dona is admitted for \( \frac{1}{5} \) share in future profits. Therefore, the old partners together will share: \[ 1 - \frac{1}{5} = \frac{4}{5} \]
Step 3: Determine total capital of the new firm.
The capital of Rs. 3,00,000 corresponds to \( \frac{4}{5} \) of the total capital. \[ \text{Total capital of the firm} = \frac{3,00,000}{4} \times 5 \] \[ = 75,000 \times 5 = 3,75,000 \]
Step 4: Calculate Dona's capital contribution.
Dona's share = \( \frac{1}{5} \) of total capital. \[ \text{Dona's capital} = \frac{1}{5} \times 3,75,000 \] \[ = 75,000 \]
Step 5: Conclusion.
Therefore, Dona must bring Rs. 75,000 as capital to maintain the proportion of the profit-sharing ratio.
Final Answer: Rs. 75,000.