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Q.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 1st April, 2023 for 1/5 th 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

CBSECBSE Class XII Board 2024MCQ· 1mImportance★★★★★
✓ Free question

Aadi brings ₹1,50,000 for a 1/5 share, so the firm's capitalised value is ₹1,50,000 × 5 = ₹7,50,000. The net worth of the firm after admission (all partners' capital) is ₹2,00,000 + ₹1,80,000 + ₹1,50,000 = ₹5,30,000. Hidden goodwill = ₹7,50,000 − ₹5,30,000 = ₹2,20,000. Correct option: (B).

Concept: Hidden Goodwill on Admission

When a new partner brings in capital for an agreed share of profits but no separate amount is given for goodwill, the goodwill is "hidden" inside the capital he brings. It is found by the capitalisation method: the capital the new partner pays, scaled up by his share, gives the total value the firm is worth (its capitalised value); the goodwill is the excess of that value over the firm's actual net worth (net assets).

Step-by-Step Solution

Step 1 — Capitalised value of the firm (based on Aadi's capital)

Aadi brings ₹1,50,000 for a 1/5 share. If 1/5 of the firm is worth ₹1,50,000, the whole firm is worth:

Capitalised value = Aadi's capital × (reciprocal of his share) = 1,50,000 × 5/1 = ₹7,50,000

Step 2 — Net worth (net assets) of the firm after admission

The net worth is the total capital actually standing in the firm once Aadi joins — the two old partners' capital plus Aadi's capital:

PartnerCapital (₹)
Seema2,00,000
Laksh1,80,000
Aadi1,50,000
Net worth of firm5,30,000

Step 3 — Hidden goodwill

Goodwill = Capitalised value − Net worth = 7,50,000 − 5,30,000 = ₹2,20,000

Watch out

The most common error is to subtract only the OLD partners' capital (₹3,80,000) and report ₹3,70,000 (option C). Aadi's own ₹1,50,000 is part of the firm's net worth after his admission, so it must be included — ₹3,70,000 is the classic trap option, not the answer.

✓Final answer

The goodwill of the firm on Aadi's admission is ₹2,20,000, which corresponds to option (B).

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