Question

X and Y are partners sharing profits in the ratio of \(2:1\). They admit Z into partnership for \( \frac{1}{4} \) share in profits for which he brings Rs.20,000 as his share of capital. Hence, the adjusted capitals of X and Y will be:

• A. Rs.40,000 and Rs.20,000 respectively.
• B. Rs.32,000 and Rs.28,000 respectively.
• C. Rs.60,000 and Rs.30,000 respectively.
• D. Rs.20,000 and Rs.40,000 respectively.

Hint:

To find total capital: \[ \text{Total Capital} = \frac{\text{Capital brought by new partner}} {\text{Share acquired}} \] Then distribute remaining capital among old partners in their profit-sharing ratio.

Answer 1

The Correct Option is C

Concept: When a new partner is admitted, the total capital of the firm can be determined on the basis of the capital introduced by the new partner and his share in profits. The old partners' adjusted capitals are then calculated according to their profit-sharing ratio.

Step 1: Calculate total capital of the firm.
Z brings: \[ Rs.20,000 \] for: \[ \frac{1}{4} \text{ share of profit} \] Therefore, total capital of the firm: \[ = \frac{20,000}{1/4} \] \[ = Rs.80,000 \]

Step 2: Calculate old partners' combined capital.
After admission, Z's capital: \[ Rs.20,000 \] Thus, combined capital of X and Y: \[ 80,000 - 20,000 \] \[ = Rs.60,000 \]

Step 3: Distribute capital between X and Y.
Old profit-sharing ratio: \[ 2:1 \] Total ratio: \[ 2+1=3 \] Capital of X: \[ 60,000 \times \frac{2}{3} \] \[ = Rs.40,000 \] Capital of Y: \[ 60,000 \times \frac{1}{3} \] \[ = Rs.20,000 \]

Step 4: Identify the correct option.
Thus, adjusted capitals are: \[ \boxed{Rs.40,000 \text{ and } Rs.20,000} \] Hence, the correct answer is: \[ \boxed{(A)} \]