1 markMCQSection A

Soni and Kush were partners in a firm sharing profits and losses in the ratio of 4 : 5. Hitesh was admitted as a new partner for 1/5th share in the profits of the firm. After all adjustments regarding general reserve, goodwill, and gain on revaluation of assets and reassessment of liabilities, the balances in capital accounts of Soni and Kush were Rs. 7,00,000 and Rs. 13,00,000 respectively. Hitesh brought in proportionate capital for his 1/5th share in the profits of the firm. The amount of proportionate capital brought in by Hitesh was :

Q: Soni and Kush were partners in a firm sharing profits and losses in the ratio of 4 : 5. Hitesh was admitted as a new partner for 1/5th share in the profits of the firm. After all adjustments regarding general reserve, goodwill, and gain on revaluation of assets and reassessment of liabilities, the balances in capital accounts of Soni and Kush were Rs. 7,00,000 and Rs. 13,00,000 respectively. Hitesh brought in proportionate capital for his 1/5th share in the profits of the firm. The amount of proportionate capital brought in by Hitesh was :

**Correct option: (C) Rs. 5,00,000.** Combined adjusted capital of old partners (Soni + Kush) = Rs. 7,00,000 + Rs. 13,00,000 = Rs. 20,00,000, representing their combined 4/5th share (since Hitesh takes 1/5th). - $\text{Total capital of new firm} = \text{Rs. }20,00,000 \times 5/4 = \text{Rs. }25,00,000$ - $\text{Hitesh's proportionate capital (1/5th share)} = \text{Rs. }25,00,000 \times 1/5 = $**Rs. 5,00,000**

Reconstitution of a Partnership Firm: Admission of a Partner

Admission of a Partner — Calculation of New Partner's Proportionate Capital

Options

(A)Rs. 25,00,000

(B)Rs. 20,00,000

(C)Rs. 5,00,000

(D)Rs. 10,00,000

Official Answer

Correct option: (C) Rs. 5,00,000.

Combined adjusted capital of old partners (Soni + Kush) = Rs. 7,00,000 + Rs. 13,00,000 = Rs. 20,00,000, representing their combined 4/5th share (since Hitesh takes 1/5th).

$\text{Total capital of new firm} = \text{Rs. }20,00,000 \times 5/4 = \text{Rs. }25,00,000$
$\text{Hitesh's proportionate capital (1/5th share)} = \text{Rs. }25,00,000 \times 1/5 =$ Rs. 5,00,000

admission of a partnerproportionate capitalnew partner's capitaladjusted capitaltotal capital of new firmreconstitution of partnership

Marking Scheme

11 mark: for correctly identifying option (C) with the working: $\text{total capital} = \text{Rs. }20,00,000 \times 5/4 = \text{Rs. }25,00,000; \text{Hitesh's capital} = 1/5 \times \text{Rs. }25,00,000 = \text{Rs. }5,00,000$ .

Hint

Old partners' adjusted capital represents (1 − new partner's share) of total firm capital; gross up to 100% first, then multiply by the new partner's share.

Quick Oral Answer

Since Soni and Kush's combined adjusted capital of Rs. 20,00,000 represents their 4/5th share, the total firm capital works out to Rs. 25,00,000, so Hitesh's 1/5th share comes to Rs. 5,00,000.

Analysis & Explanation

Concept: When a new partner is admitted and asked to bring proportionate capital for their share, the total capital of the new firm is first derived from the adjusted (post-adjustment) capitals of the old partners, since their combined capital represents the remaining share (1 − new partner's share).

Working:

Combined capital of Soni and Kush (after all adjustments) = Rs. 20,00,000 → this represents 4/5th of total firm capital (since Hitesh gets 1/5th).
$\text{Total capital of the new firm} = \text{Rs. }20,00,000 \times 5/4 = \text{Rs. }25,00,000$ .
$\text{Hitesh's share of total capital} = 1/5 \times \text{Rs. }25,00,000 = \text{Rs. }5,00,000$ .

Why other options are wrong:

(A) Rs. 25,00,000 is the TOTAL capital of the new firm, not Hitesh's share alone.
(B) Rs. 20,00,000 is merely the combined old partners' capital, not scaled to the new total.
(D) Rs. 10,00,000 would result from wrongly using 2/5th instead of 1/5th as Hitesh's share.

Application: This method (deriving the new partner's capital from old partners' adjusted capitals) is used whenever the question states that the new partner brings in capital 'proportionate to' or 'in the same proportion as' their share of profit.

Common Mistakes

1Treating Rs. 20,00,000 itself as the total capital of the new firm instead of grossing it up by 5/4.
2Multiplying the total new-firm capital by the wrong fraction (e.g., 4/5 instead of 1/5) for Hitesh's share.
3Forgetting that the old partners' balances given are already POST-adjustment (after reserve, goodwill and revaluation), so no further adjustment is needed to them before scaling up.

Interesting Facts

This 'proportionate capital' method ensures that all partners' capitals are in exact alignment with their new profit-sharing ratio immediately upon admission, avoiding future disputes over capital-based entitlements like interest on capital.

CBSE frequently frames this as an MCQ testing whether students correctly identify which fraction (old partners' combined share, not the new partner's share) the given capital figures represent.

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Frequently Asked Questions

How do you find the total capital of the new firm when a new partner brings proportionate capital?

Gross up the combined adjusted capital of the old partners by dividing by their combined share (equivalently, multiply by the reciprocal of their combined share). Here, old partners hold 4/5th, so Total Capital = Rs. 20,00,000 × 5/4 = Rs. 25,00,000.

Why are Soni's and Kush's capitals already 'adjusted' before this calculation?

The question states these balances are AFTER all adjustments for general reserve, goodwill, and revaluation gains/losses — meaning their capital accounts already reflect the correct amounts as per the new arrangement, so they can be directly used to derive total firm capital.