Question

Seema and Laksh were partners in a firm sharing profits and losses in the ratio of \( 2 : 1 \). Their capitals were ₹ 2,00,000 and ₹ 1,80,000 respectively. They admitted Aadi as a new partner on 1\textsuperscript{st April, 2023, for \( \frac{1}{5} \) share in future profits. Aadi brought ₹ 1,50,000 as his share of capital. The goodwill of the firm on Aadi’s admission will be:}

• A. ₹ 7,50,000
• B. ₹ 2,20,000
• C. ₹ 3,70,000
• D. ₹ 1,50,000

Hint:

When calculating goodwill on a partner's admission, always deduct the partner's capital contribution included in the goodwill from the total calculated goodwill.

Answer 1

The Correct Option is B

1. Determine Total Capital of the Firm: Aadi’s share = \( \frac{1}{5} \). Total capital of the firm is calculated based on Aadi’s contribution: \[ \text{Total Capital} = \frac{\text{Aadi's Capital}}{\text{Aadi's Share}} = \frac{₹ 1,50,000}{\frac{1}{5}} = ₹ 7,50,000. \] 2. Calculate the Goodwill: Goodwill is the difference between the total capital and the existing partners' capital: \[ \text{Goodwill} = \text{Total Capital} - (\text{Seema's Capital} + \text{Laksh's Capital}). \] Substituting values: \[ \text{Goodwill} = ₹ 7,50,000 - (₹ 2,00,000 + ₹ 1,80,000) = ₹ 7,50,000 - ₹ 3,80,000 = ₹ 3,70,000. \] 3. Adjustment for Aadi’s Contribution to Goodwill: Aadi’s goodwill share is already included in his contribution. Subtract Aadi’s contribution from the calculated goodwill: \[ \text{Goodwill} = ₹ 3,70,000 - ₹ 1,50,000 = ₹ 2,20,000. \]