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:

The goodwill is calculated by comparing the implied total capital of the firm with the combined capital of the existing partners.

Answer 1

The Correct Option is B

Aadi's investment of ₹ 1,50,000 represents a \( \frac{1}{5} \) stake in the firm. Consequently, the firm's total capital is determined as follows: \[Total Capital of the Firm} = 1,50,000 \times \frac{5}{1} = ₹ 7,50,000.\] The combined capital contributed by Seema and Laksh amounts to: \[Seema’s Capital} + Laksh’s Capital} = 2,00,000 + 1,80,000 = ₹ 3,80,000.\] The firm's goodwill is calculated by subtracting the existing partners' capital from the total capital: \[Goodwill} = 7,50,000 - 3,80,000 = ₹ 3,70,000.\] Given Aadi's \( \frac{1}{5} \) share of the total goodwill: \[Aadi’s Share of Goodwill} = \frac{1}{5} \times 3,70,000 = ₹ 74,000.\] After goodwill adjustments, the total goodwill recorded in the books is ₹ 2,20,000.