CBSE Class 12 Accountancy: Reconstitution of a Partnership Firm – Retirement/Death of a Partner NCERT Solutions

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NCERT Solutions PDF Class 12 PDF

This section provides comprehensive NCERT Solutions for Class 12 Accountancy, focusing on Chapter 4: Reconstitution of a Partnership Firm – Retirement/Death of a Partner. It covers essential concepts like calculating the gaining ratio and determining the new profit-sharing ratio when a partner retires or passes away. The solutions offer step-by-step explanations for various scenarios, helping students understand how to adjust profit-sharing ratios and calculate the gains of the continuing partners. These detailed solutions are designed to aid students in mastering the complexities of partnership reconstitution, ensuring a thorough understanding for their board examinations and future studies in accounting.

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BoardCBSE
ClassClass 12
SubjectAccountancy
Session2026
LanguageEnglish
TypeNCERT Solutions
ChapterPart 1 - 4. Reconstitution of a Partnership Firm – Retirement-Death of a Partner

Chapter summary

This chapter's NCERT Solutions for Class 12 Accountancy focus on the reconstitution of a partnership firm due to the retirement or death of a partner. It provides detailed explanations and calculations for determining the gaining ratio and the new profit-sharing ratio among the remaining partners. The solutions cover different scenarios, including how the retiring partner's share is acquired by the continuing partners, and offer practice problems to solidify understanding of these crucial adjustments in partnership accounting.

Learning outcomes

  • Understand the concept of gaining ratio in partnership reconstitution.
  • Calculate the gaining ratio when a partner retires or dies.
  • Determine the new profit-sharing ratio of continuing partners.
  • Apply different methods for calculating new profit shares based on acquisition ratios.
  • Solve problems involving changes in profit-sharing ratios after partner retirement/death.

Topics covered

Paper topics

  • Gaining Ratio Calculation
  • New Profit Sharing Ratio
  • Retirement of a Partner
  • Death of a Partner
  • Adjustment of Profit Shares
  • Partnership Reconstitution

Important topics

  • Gaining Ratio
  • New Profit Sharing Ratio
  • Acquisition of Retiring Partner's Share
  • Impact of Retirement/Death on Profit Sharing

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Questions and Solutions

Question 1

Anita, Jaya and Nisha are partners sharing profits and losses in the ratio of 1:1:1. Jaya retires from the firm. Anita and Nisha decided to share the profit in future in the ratio 4 :3. Calculate the gaining ratio.
Solution:

The gaining ratio is calculated by subtracting the old profit-sharing ratio from the new profit-sharing ratio for each continuing partner.

Old Profit Sharing Ratio (Anita : Jaya : Nisha) = 1:1:1

Jaya retires. Her share was \(\frac{1}{3}\).

New Profit Sharing Ratio (Anita : Nisha) = 4:3

The total share of Anita and Nisha in the new ratio is \(\frac{4}{7}\) and \(\frac{3}{7}\) respectively.

The old share of Anita was \(\frac{1}{3}\) and the old share of Nisha was \(\frac{1}{3}\).

Anita's gain = New Ratio - Old Ratio

\text{Anita's gain} = \frac{4}{7} - \frac{1}{3} = \frac{(4 \times 3) - (1 \times 7)}{21} = \frac{12 - 7}{21} = \frac{5}{21}

Nisha's gain = New Ratio - Old Ratio

\text{Nisha's gain} = \frac{3}{7} - \frac{1}{3} = \frac{(3 \times 3) - (1 \times 7)}{21} = \frac{9 - 7}{21} = \frac{2}{21}

Therefore, the gaining ratio between Anita and Nisha is 5:2.

Question 2

Azad, Vijay and Amit are partners sharing profits and losses in the proportion of 1/4, 1/8, and 10/16 respectively. Calculate the new profit sharing ratio between continuing partners if (a) Azad retires; (b) Vijay retires; (c) Amit retires.
Solution:

First, let's express the profit-sharing ratios in a common denominator to simplify them.

Azad's share = \(\frac{1}{4}\)

Vijay's share = \(\frac{1}{8}\)

Amit's share = \(\frac{10}{16}\)

To find a common denominator, we can use 16.

Azad's share = \(\frac{1 \times 4}{4 \times 4} = \frac{4}{16}\)

Vijay's share = \(\frac{1 \times 2}{8 \times 2} = \frac{2}{16}\)

Amit's share = \(\frac{10}{16}\)

The original profit-sharing ratio (Azad : Vijay : Amit) is 4:2:10, which simplifies to 2:1:5.

(a) If Azad retires:

The continuing partners are Vijay and Amit. Their original shares were in the ratio 1:5. Since Azad's share is gone, the remaining partners will continue to share profits in their existing proportion relative to each other. Thus, the new profit-sharing ratio between Vijay and Amit is 1:5.

(b) If Vijay retires:

The continuing partners are Azad and Amit. Their original shares were in the ratio 2:5. Since Vijay's share is gone, the new profit-sharing ratio between Azad and Amit is 2:5.

(c) If Amit retires:

The continuing partners are Azad and Vijay. Their original shares were in the ratio 2:1. Since Amit's share is gone, the new profit-sharing ratio between Azad and Vijay is 2:1.

Question 3

Calculate the gaining ratio in each of the above situations.
Solution:

The gaining ratio is calculated as: Gaining Ratio = New Ratio – Old Ratio.

The original profit-sharing ratio (Azad : Vijay : Amit) is 2:1:5.

(a) If Azad retires:

The new profit-sharing ratio between Vijay and Amit is 1:5.

Vijay's old share = \(\frac{1}{8}\) (from 2:1:5, total 8 parts, Vijay has 1 part, but the source uses 1/8 directly, let's use the simplified ratio 2:1:5 for consistency with the question's calculation method)

Let's re-evaluate using the simplified ratio 2:1:5. The total parts are 2+1+5 = 8. So, Old shares are Azad = 2/8, Vijay = 1/8, Amit = 5/8.

If Azad retires, the new ratio between Vijay and Amit is 1:5. This means their new shares are Vijay = \(\frac{1}{6}\) and Amit = \(\frac{5}{6}\).

Vijay's gain = New Share - Old Share

\text{Vijay's gain} = \frac{1}{6} - \frac{1}{8} = \frac{4 - 3}{24} = \frac{1}{24}

Amit's gain = New Share - Old Share

\text{Amit's gain} = \frac{5}{6} - \frac{5}{8} = \frac{20 - 15}{24} = \frac{5}{24}

The gaining ratio is 1:5.

(b) If Vijay retires:

The new profit-sharing ratio between Azad and Amit is 2:5. Their new shares are Azad = \(\frac{2}{7}\) and Amit = \(\frac{5}{7}\).

Azad's old share = \(\frac{2}{8}\)

Amit's old share = \(\frac{5}{8}\)

Azad's gain = New Share - Old Share

\text{Azad's gain} = \frac{2}{7} - \frac{2}{8} = \frac{16 - 14}{56} = \frac{2}{56}

Amit's gain = New Share - Old Share

\text{Amit's gain} = \frac{5}{7} - \frac{5}{8} = \frac{40 - 35}{56} = \frac{5}{56}

The gaining ratio is 2:5.

(c) If Amit retires:

The new profit-sharing ratio between Azad and Vijay is 2:1. Their new shares are Azad = \(\frac{2}{3}\) and Vijay = \(\frac{1}{3}\).

Azad's old share = \(\frac{2}{8}\)

Vijay's old share = \(\frac{1}{8}\)

Azad's gain = New Share - Old Share

\text{Azad's gain} = \frac{2}{3} - \frac{2}{8} = \frac{16 - 6}{24} = \frac{10}{24}

Vijay's gain = New Share - Old Share

\text{Vijay's gain} = \frac{1}{3} - \frac{1}{8} = \frac{8 - 3}{24} = \frac{5}{24}

The gaining ratio is 10:5, which simplifies to 2:1.

Question 4

Anu, Prabha and Milli are partners sharing profits and losses in the ratio of 1:1:1. Anu retires. Calculate the future profit sharing ratio of continuing partners and gaining ratio if they agree to acquire her share: (a) in the ratio of 5:3; (b) equally.
Solution:

Original Profit Sharing Ratio (Anu : Prabha : Milli) = 1:1:1

Anu retires. Her share is \(\frac{1}{3}\).

The continuing partners are Prabha and Milli.

(a) If Anu's share is acquired by Prabha and Milli in the ratio of 5:3:

Prabha's gain = Anu's share \(\times\) Prabha's share in acquisition ratio

\text{Prabha's gain} = \frac{1}{3} \times \frac{5}{5+3} = \frac{1}{3} \times \frac{5}{8} = \frac{5}{24}

Milli's gain = Anu's share \(\times\) Milli's share in acquisition ratio

\text{Milli's gain} = \frac{1}{3} \times \frac{3}{5+3} = \frac{1}{3} \times \frac{3}{8} = \frac{3}{24}

Prabha's old share = \(\frac{1}{3}\)

Milli's old share = \(\frac{1}{3}\)

Prabha's new share = Prabha's old share + Prabha's gain

\text{Prabha's new share} = \frac{1}{3} + \frac{5}{24} = \frac{8}{24} + \frac{5}{24} = \frac{13}{24}

Milli's new share = Milli's old share + Milli's gain

\text{Milli's new share} = \frac{1}{3} + \frac{3}{24} = \frac{8}{24} + \frac{3}{24} = \frac{11}{24}

The new profit-sharing ratio between Prabha and Milli is 13:11.

The gaining ratio is 5:3.

(b) If Anu's share is acquired by Prabha and Milli equally:

Prabha's gain = Anu's share \(\times\) Prabha's share in acquisition ratio

\text{Prabha's gain} = \frac{1}{3} \times \frac{1}{2} = \frac{1}{6}

Milli's gain = Anu's share \(\times\) Milli's share in acquisition ratio

\text{Milli's gain} = \frac{1}{3} \times \frac{1}{2} = \frac{1}{6}

Prabha's old share = \(\frac{1}{3}\)

Milli's old share = \(\frac{1}{3}\)

Prabha's new share = Prabha's old share + Prabha's gain

\text{Prabha's new share} = \frac{1}{3} + \frac{1}{6} = \frac{2}{6} + \frac{1}{6} = \frac{3}{6}

Milli's new share = Milli's old share + Milli's gain

\text{Milli's new share} = \frac{1}{3} + \frac{1}{6} = \frac{2}{6} + \frac{1}{6} = \frac{3}{6}

The new profit-sharing ratio between Prabha and Milli is 3:3, which simplifies to 1:1.

The gaining ratio is 1:1.

Question 5

Rahul, Robin and Rajesh are partners sharing profits in the ratio of 3:2:1. Calculate the new profit sharing ratio of the remaining partners if (i) Rahul retires; (ii) Robin retires; (iii) Rajesh retires.
Solution:

Original Profit Sharing Ratio (Rahul : Robin : Rajesh) = 3:2:1. The total shares are 3+2+1 = 6.

So, Rahul's share = \(\frac{3}{6}\), Robin's share = \(\frac{2}{6}\), Rajesh's share = \(\frac{1}{6}\).

When a partner retires, the remaining partners continue to share profits in the same ratio as before, unless a new agreement is made.

(i) If Rahul retires:

The continuing partners are Robin and Rajesh. Their original shares were \(\frac{2}{6}\) and \(\frac{1}{6}\). Since there is no new agreement mentioned, they will continue to share profits in their existing ratio. The new profit-sharing ratio between Robin and Rajesh will be 2:1.

(ii) If Robin retires:

The continuing partners are Rahul and Rajesh. Their original shares were \(\frac{3}{6}\) and \(\frac{1}{6}\). The new profit-sharing ratio between Rahul and Rajesh will be 3:1.

(iii) If Rajesh retires:

The continuing partners are Rahul and Robin. Their original shares were \(\frac{3}{6}\) and \(\frac{2}{6}\). The new profit-sharing ratio between Rahul and Robin will be 3:2.

Question 6

Puja, Priya, Pratistha are partners sharing profits and losses in the ratio of 5:3:2. Priya retires. Her share is taken by Puja and Pratistha in the ratio of 2:1. Calculate the new profit sharing ratio. (Note: The provided solution indicates Puja retires, not Priya. Assuming Puja retires based on the solution's calculation.)
Solution:

Original Profit Sharing Ratio (Puja : Priya : Pratistha) = 5:3:2. Total shares = 5+3+2 = 10.

Puja's share = \(\frac{5}{10}\), Priya's share = \(\frac{3}{10}\), Pratistha's share = \(\frac{2}{10}\).

Assuming Puja retires (as per the calculation in the source):

Puja's share = \(\frac{5}{10}\).

This share is taken by Priya and Pratistha in the ratio of 2:1.

Priya's gain = Puja's share \(\times\) Priya's share in acquisition ratio

\text{Priya's gain} = \frac{5}{10} \times \frac{2}{2+1} = \frac{5}{10} \times \frac{2}{3} = \frac{10}{30}

Pratistha's gain = Puja's share \(\times\) Pratistha's share in acquisition ratio

\text{Pratistha's gain} = \frac{5}{10} \times \frac{1}{2+1} = \frac{5}{10} \times \frac{1}{3} = \frac{5}{30}

Priya's old share = \(\frac{3}{10}\)

Pratistha's old share = \(\frac{2}{10}\)

Priya's new share = Priya's old share + Priya's gain

\text{Priya's new share} = \frac{3}{10} + \frac{10}{30} = \frac{9}{30} + \frac{10}{30} = \frac{19}{30}

Pratistha's new share = Pratistha's old share + Pratistha's gain

\text{Pratistha's new share} = \frac{2}{10} + \frac{5}{30} = \frac{6}{30} + \frac{5}{30} = \frac{11}{30}

The new profit-sharing ratio between Priya and Pratistha is 19:11.

Question 7

Ashok, Anil and Ajay are partners sharing profits and losses in the ratio of 1/2, 3/10 and 1/5. Anil retires from the firm. Ashok and Ajay decide to share future profits and losses in the ratio of 3:2. Calculate the gaining ratio.
Solution:

First, convert the profit-sharing ratios to a common denominator.

Ashok's share = \(\frac{1}{2}\)

Anil's share = \(\frac{3}{10}\)

Ajay's share = \(\frac{1}{5}\)

The common denominator is 10.

Ashok's share = \(\frac{1 \times 5}{2 \times 5} = \frac{5}{10}\)

Anil's share = \(\frac{3}{10}\)

Ajay's share = \(\frac{1 \times 2}{5 \times 2} = \frac{2}{10}\)

The original profit-sharing ratio (Ashok : Anil : Ajay) is 5:3:2.

Anil retires from the firm. His share was \(\frac{3}{10}\).

Ashok and Ajay decide to share future profits in the ratio of 3:2. This is their new profit-sharing ratio.

Ashok's new share = \(\frac{3}{3+2} = \frac{3}{5}\)

Ajay's new share = \(\frac{2}{3+2} = \frac{2}{5}\)

The gaining ratio is calculated as: Gaining Ratio = New Ratio – Old Ratio.

Ashok's old share = \(\frac{5}{10}\)

Ajay's old share = \(\frac{2}{10}\)

Ashok's gain = Ashok's new share - Ashok's old share

\text{Ashok's gain} = \frac{3}{5} - \frac{5}{10} = \frac{6}{10} - \frac{5}{10} = \frac{1}{10}

Ajay's gain = Ajay's new share - Ajay's old share

\text{Ajay's gain} = \frac{2}{5} - \frac{2}{10} = \frac{4}{10} - \frac{2}{10} = \frac{2}{10}

The gaining ratio between Ashok and Ajay is 1:2.

Common mistakes

  • Incorrectly calculating the new ratio instead of the gaining ratio.
  • Errors in fraction arithmetic when calculating gains or new shares.
  • Confusing the old ratio with the new ratio when calculating gains.
  • Misinterpreting the ratio in which the continuing partners acquire the retiring partner's share.

Revision tips

  • Focus on the formula: Gaining Ratio = New Ratio – Old Ratio.
  • Practice calculating the new profit-sharing ratio under different acquisition scenarios.
  • Ensure all calculations involving fractions are accurate.
  • Review the examples carefully to understand how each partner's gain is computed.

Practice MCQs

Q1. What is the formula to calculate the gaining ratio?

Q2. If the new ratio is greater than the old ratio for a partner, they have:

Q3. In the absence of any agreement, the continuing partners acquire the retiring partner's share:

Q4. What does a positive result in (New Ratio - Old Ratio) signify?

Frequently asked questions

What is the gaining ratio in partnership accounting?

The gaining ratio is the ratio in which the continuing partners acquire the share of the retiring or deceased partner. It is calculated as: Gaining Ratio = New Ratio – Old Ratio.

How is the new profit-sharing ratio calculated when a partner retires?

The new profit-sharing ratio is determined by adding the gaining share of each continuing partner to their original share. If the retiring partner's share is acquired in a specific ratio, that ratio is used to calculate the gains first.

What happens if the problem doesn't specify how the continuing partners acquire the retiring partner's share?

In the absence of a specific agreement, it is assumed that the continuing partners will acquire the retiring partner's share in their old profit-sharing ratio.

Why is calculating the gaining ratio important?

The gaining ratio is crucial for adjusting the capital accounts of the continuing partners. Any goodwill that remains to be adjusted will be debited to the gaining partners and credited to the sacrificing partners (if any).

Are the concepts of retirement and death of a partner treated the same way for profit-sharing ratio adjustments?

Yes, for the purpose of calculating the gaining ratio and the new profit-sharing ratio, the methods are generally the same whether a partner retires or dies, assuming the deceased partner's share is to be distributed among the remaining partners.

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