Solutions of DK Goel Class 12 Chapter 4 Retirement of Partner [2025-26]
Question 1:
(A). A, B and C are partners sharing profits in the ratio of 6 : 5 : 4. Calculate new profit sharing ratios if (i) A retires; (ii) B retires; (iii) C retires.
Solution
A : B : C = 6 : 5 : 4
(i) A retires
\(\quad\) New Profit-sharing ratio = 5 : 4
(ii) B retires
\(\quad\) New Profit-sharing ratio = 6 : 4
(i) C retires
\(\quad\) New Profit-sharing ratio = 6 : 5
(B). A, B, C and D are partners sharing profits in the ratio of 5 : 3 : 1 : 2. Calculate the new profit sharing ratio if B and C retire from the firm.
Solution
A : B : C : D = 5 : 3 : 1 : 2
B and C retires
A : D = 5 : 2
Question 2:
X, Y and Z are partners sharing profits in the ratio of \(\frac{2}{3} : \frac{1}{4} : \frac{1}{12}\). Calculate the new ratio if X retires.
Solution
X : Y : Z = \(\frac{2}{3} : \frac{1}{4} : \frac{1}{12}\) = 8 : 3 : 1
X retires
New share = 3 : 1
Question 3:
L, M and O were partners in a firm sharing profits in the ratio of 3 : 2 : 2. M retired and his share was divided equally between L and O. Calculate the new profit sharing ratio of L and O.
Solution
L : M : O = 3 : 2 : 2
M retires and his share is divided equally between L and O.
L gain = \(\frac{2}{7} \times \frac{1}{2} = \frac{2}{14}\)
O gain = \(\frac{2}{7} \times \frac{1}{2} = \frac{2}{14}\)
L’s new share = \(\frac{3}{7} + \frac{2}{14} = \frac{8}{14}\)
O’s new share = \(\frac{2}{7} + \frac{2}{14} = \frac{6}{14}\)
New Profit-sharing
= 8 : 6 or 4 : 3
Question 4:
A, B and C are partners sharing profits in the ratio of 4 : 3 : 2. B retires and his share was taken up by A and C in the ratio of 3 : 2. Find out the new ratio.
Solution
A : B : C = 4 : 3 : 2
B retires and his share was taken up by A and C in the ratio of 3 : 2.
A gain = \(\frac{3}{9} \times \frac{3}{5} = \frac{9}{45}\)
C gain = \(\frac{3}{9} \times \frac{2}{5} = \frac{6}{45}\)
A’s new share = \(\frac{4}{9} + \frac{9}{45} = \frac{29}{45}\)
C’s new share = \(\frac{2}{9} + \frac{6}{45} = \frac{16}{14}\)
New Profit-sharing
= 29 : 16
Question 5:
A, B and C are partners sharing profits in the ratio of 4 : 3 : 1. A retires and his share is taken over by B and C equally. Calculate the new ratio.
Solution
A : B : C = 4 : 3 : 1
A retires and his share is taken over by B and C equally.
B gain = \(\frac{4}{8} \times \frac{1}{2} = \frac{4}{16}\)
C gain = \(\frac{4}{8} \times \frac{1}{2} = \frac{4}{16}\)
B’s new share = \(\frac{3}{8} + \frac{4}{16} = \frac{10}{16}\)
C’s new share = \(\frac{1}{8} + \frac{4}{16} = \frac{6}{16}\)
New Profit-sharing
= 10 : 6 = 5 : 3
Question 6:
X, Y and Z are partners sharing in the ratio of 2 : 2 : 1. Y retires and his share is entirely taken by Z. Calculate the new ratio.
Solution
X : Y : Z = 2 : 2 : 1
Y retires and his share is entirely taken by Z.
Z gain = \(\frac{2}{5}\)
X’s new share = \frac{2}{5}\)
Z’s new share = \(\frac{1}{5} + \frac{2}{5} = \frac{3}{5}\)
New Profit-sharing
= 2 : 3
Question 7:
Aman, Naman and Neel were partners in a firm sharing profits in the ratio of 1 : 2 : 1. Neel retires and he surrenders 2/3rd of his share in favour of Aman and the remaining share in favour of Naman.
Calculate the new profit sharing ratio of Aman and Naman.
Solution
Aman : Naman : Neel = 1 : 2 : 1
Neel retires and he surrenders 2/3rd of his share in favour of Aman and the remaining share in favour of Naman.
Aman gain = \(\frac{1}{4} \times \frac{2}{3} = \frac{2}{12}\)
Naman gain = \(\frac{1}{4} – \frac{2}{12} = \frac{1}{12}\)
Aman’s new share = \(\frac{1}{4} + \frac{2}{12} = \frac{5}{12}\)
Naman’s new share = \(\frac{2}{4} + \frac{1}{12} = \frac{7}{12}\)
New profit-sharing ratio
= 5 : 7
Question 8:
P, Q, R and S were partners in a firm sharing profits and losses in the ratio of 4 : 3 : 2 : 1. On 31st March, 2022, P retired from the firm. P’s share was taken over by Q, R and S in the ratio of 1 : 2 : 3. Calculate the new profit sharing ratio of Q, R and S.
Solution
p : Q : R : S = 4 : 3 : 2 : 1
P retires and his share is taken over by Q, R and S in the ratio of 1 : 2 : 3.
Q gain = \(\frac{4}{10} \times \frac{1}{6} = \frac{4}{60}\)
R gain = \(\frac{4}{10} \times \frac{2}{6} = \frac{8}{60}\)
S gain = \(\frac{4}{10} \times \frac{3}{6} = \frac{12}{60}\)
Q’s new share = \(\frac{3}{10} + \frac{4}{60} = \frac{22}{60}\)
R’s new share = \(\frac{2}{10} + \frac{8}{60} = \frac{20}{60}\)
S’s new share = \(\frac{1}{10} + \frac{12}{60} = \frac{18}{60}\)
New profit-sharing ratio of Q, R and S
= 22 : 20 : 18 = 11 : 10 : 9
Question 9:
P, Q and R are in partnership sharing profits and losses as \(\frac{1}{2}\), \(\frac{2}{6}\) and \(\frac{1}{6}\) respectively. R retires and his share is taken by P and Q in the ratio of 2 : 1. Immediately, S is admitted for 1/4th share of profit, 1/3rd of which was given by P and the remaining share was taken equally from P and Q. Calculate new profit sharing after S’s admission.
Solution
P : Q : R = \(\frac{1}{2} :\frac{2}{6} : \frac{1}{6}\) = 3 : 2 : 1
R retires and his share is taken by P and Q in the ratio of 2 : 1.
P gain = \(\frac{1}{6} \times \frac{2}{3} = \frac{2}{18}\)
Q gain = \(\frac{1}{6} \times \frac{1}{3} = \frac{1}{18}\)
P’s new share = \(\frac{3}{6} + \frac{2}{18} = \frac{11}{18}\)
Q’s new share = \(\frac{2}{6} + \frac{1}{18} = \frac{7}{18}\)
New profit-sharing ratio of Q, R and S
= 11 : 7
Question 9:
P, Q and R are in partnership sharing profits and losses as \(\frac{1}{2}\), \(\frac{2}{6}\) and \(\frac{1}{6}\) respectively. R retires and his share is taken by P and Q in the ratio of 2 : 1. Immediately, S is admitted for 1/4th share of profit, 1/3rd of which was given by P and the remaining share was taken equally from P and Q. Calculate new profit sharing after S’s admission.
Solution
P : Q : R = \(\frac{1}{2} :\frac{2}{6} : \frac{1}{6}\) = 3 : 2 : 1
R retires and his share is taken by P and Q in the ratio of 2 : 1.
P gain = \(\frac{1}{6} \times \frac{2}{3} = \frac{2}{18}\)
Q gain = \(\frac{1}{6} \times \frac{1}{3} = \frac{1}{18}\)
P’s new share = \(\frac{3}{6} + \frac{2}{18} = \frac{11}{18}\)
Q’s new share = \(\frac{2}{6} + \frac{1}{18} = \frac{7}{18}\)
New profit-sharing ratio of P, and Q
= 11 : 7
S is admitted for 1/4th share of profit, 1/3rd of which was given by P and the remaining share was taken equally from P and Q.
S acquries from P = \(\frac{1}{4}\times \frac{1}{3} = \frac{1}{12}\)
remaining share = \(\frac{1}{4} – \frac{1}{12} = \frac{2}{12}\)
Out of remaining share, S acquires from P = \(\frac{2}{12} \times \frac{1}{2} = \frac{2}{24}\)
& from Q = \(\frac{2}{12} \times \frac{1}{2} = \frac{2}{24}\)
P’s new share = \(\frac{11}{18} – \frac{1}{2} – \frac{2}{24}= \frac{44 – 6 – 6}{72} = \frac{32}{72}\)
Q’s new share = \(\frac{7}{18} – \frac{2}{24}= \frac{28 – 6}{72} = \frac{22}{72}\)
New Profit-sharing ratio of P, Q & S
= \(\frac{32}{72} : \frac{22}{72} : \frac{1}{4}\) = 32 : 22 : 18 = 16 : 11 : 9
Question 10:
(A). A, B and C were partners sharing profits in the ratio of 7 : 5 : 3. Find out the gaining ratio and new ratios when (i) A retires, (ii) B retires or (iii) C retires.
Solution
A : B : C = 7 : 5 : 3
(i) A retires
\(\quad\) New Profit-sharing ratio = 5 : 3
B gain = \(\frac{5}{8} – \frac{5}{15} = \frac{75 – 40}{120} = \frac{35}{120}\)
C gain = \(\frac{3}{8} – \frac{3}{15} = \frac{45 – 24}{120} = \frac{21}{120}\)
Gaining ratio of B & C = 35 : 21 = 5 : 3
(ii) B retires
\(\quad\) New Profit-sharing ratio = 7 : 3
A gain = \(\frac{7}{8} – \frac{7}{15} = \frac{105 – 56}{120} = \frac{49}{120}\)
C gain = \(\frac{3}{8} – \frac{3}{15} = \frac{45 – 24}{120} = \frac{21}{120}\)
Gaining ratio of A & C = 49 : 21 = 7 : 3
(i) C retires
\(\quad\) New Profit-sharing ratio = 7 : 5
A gain = \(\frac{7}{8} – \frac{7}{15} = \frac{105 – 56}{120} = \frac{49}{120}\)
B gain = \(\frac{5}{8} – \frac{5}{15} = \frac{75 – 40}{120} = \frac{35}{120}\)
Gaining ratio of A & C = 49 : 35 = 7 : 5
(B) X, Y and Z share profits in the ratio of 1/2, 3/10, 1/5. Calculate the gaining ratio and new ratios when:
(i) X dies, (ii) Y dies or (iii) Z dies.
(C). P, Q, R and S were partners sharing profits in the ratio of 5 : 4 : 3 : 1. P and S retire from the firm. Calculate the gaining ratio and new profit sharing ratio of Q and R.
Question 11:
(A) On 1st April, 2023 Ashish, Namish and Aman were partners sharing profits and losses in the ratio of 2/5, 2/5 and 1/5 respectively. On this date, Namish retires. The new profit sharing ratio of Ashish and Aman will be 3/4 and 1/4 respectively. Calculate gaining ratio.
(B). On 1st April, 2023 A, B and C were partners sharing profits and losses in the ratio of A 5/10, B 3/10 and C 2/10 respectively. On this date B retires. The new profit sharing ratio of A and C will be A 3/5 and C 2/5. Calculate gaining ratio.
Question 12:
(A) A, B and C are partners sharing profits in the ratio of 1/2 : 1/3 : 1/6. C retires and A and B decide to share future profits equally. Calculate the gaining ratio.
(B). A, B, C and D are partners sharing profits in the ratio of 5 : 4 : 3 : 2. A retires and B, C and D decide to share the profits and losses equally in future. Calculate the gaining ratio.
Question 13:
Rekha, Ruchi and Suruchi are partners. Ruchi retires. Calculate new ratio if continuing partners acquired her share in the ratio of 2 : 3. Also mention the gaining ratio.
Question 14:
X, Y and Z are partners sharing profits in the ratio of 1/9 : 1/3 and 5/9. Z retires and surrenders 3/4th of this share in favour of X and remaining in favour of Y. Calculate new ratio and gaining ratio.
Question 15:
P, Q, R and S were partners sharing profits in the ratio of 2 : 3 : 5 : 2. S retires and his share is acquired by Q and R in the ratio of 3 : 2. Calculate new ratio and gaining ratio.
Question 16:
A and B were partners sharing profits in the ratio of 5 : 3. On 1st April, 2021 they admitted C as a new partner for 1/4th share which he acquired from A and B in the ratio of 3 : 2. On 1st April 2022, another new partner D was admitted for 1/6th share which he acquires 1/10 from A and 1/15 from C. On 1st April, 2023 A dies and his share was taken over by B, C and D equally.
Calculate:
(I) New Profit sharing ratio of A, B and C on C’s admission.
(ii) New profit sharing ratio of A, B, C and D on D’s admission.
(iii) New profit sharing ratio of B, C and D on A’s death.
Question 17:
X, Y and Z are partners sharing profits in the ratio of 5 : 4 : 3. X retires from the firm and it is decided that new profit sharing ratio between Y and Z will be same as existing between X and Y. Calculate new ratio and gaining ratio.
Question 18:
(A). L, M and N are three partners sharing profits in the ratio of 4 : 3 : 2 respectively. M retires and the goodwill is valued at ₹ 1,08,000. No goodwill account appears as yet in the books of the firm. L and N will share profits in future in the ratio of 5 : 3 respectively. Pass Journal Entry for goodwill.
B) Ashok, Rakesh and Mukesh were partners sharing profits and losses in the ratio of 2 : 2 : 1. On 1st April, 2023, their goodwill was valued at ₹ 3,00,000, there being no account for it in the books. On this date Rakesh retired. Pass the Journal Entry to record goodwill.
Question 19:
A, B and C are sharing profits in the ratio of 4 : 3 : 2. Goodwill is appearing in the books at a value of ₹ 42,000. C retires and on the day of C’s retirement Goodwill is valued at ₹ 63,000. Pass the necessary Journal entries.
Question 20:
(A). P, Q and R are equal partners. Goodwill is appearing in their books at ₹ 4,00,000. R retires and on the day of R’s retirement Goodwill is valued at ₹ 2,50,000. Pass the necessary journal entries.
(B) A, B and C are partners sharing profits and losses in the ratio of 2 : 2 : 1. C decided to retire and on this date goodwill of the firm is valued at ₹ 2,00,000. Pass entries when goodwill account is already appearing in the books at ₹ 1,50,000.
Question 21:
(A). P, R and S are in partnership sharing profits 4/8, 3/8 and 1/8 respectively. It is provided under the partnership deed that on the death of any partner his share of goodwill is to be valued at one-half of the net profits credited to his account during the last 4 completed years (books of accounts are closed on 31st March).
R died on 1st April, 2022. The firm’s profits for the last 4 years were as follows: 2019 (Profits ₹ 1,20,000); 2020 (Profits ₹ 60,000); 2021 (Losses ₹ 20,000) and 2022 (Profits ₹ 80,000).
Pass journal entry for the adjustment of goodwill, assuming that profit sharing ratio between P and S in future will be 3 : 2. Show your working clearly.
Determine the amount that should be credited to R in respect of his share of goodwill.
(B). A, B, C and D are partners in a firm sharing profits and losses in the ratio o 2 : 2 : 1 : 1. A and C decided to retire from the firm. The goodwill of the firm was valued at ₹ 90,000. B and D decided to share future profits in the ratio of 5 : 3.
Pass necessary journal entry for the treatment of goodwill.
Question 22:
Arjun, Bhim and Nakul are partners sharing profits and losses in the ratio of 14 : 5 : 6 respectively. Bhim retires and surrenders his 5/25th shares in favour of Arjun. The goodwill of the firm is valued at 2 years purchase of super profits based on average profits of last 3 years. The profits for the last 3 years are ₹ 50,000, ₹ 60,000 and ₹ 55,000 respectively. The normal profits for the similar firm are ₹ 30,000. Goodwill aleardy appears in the books of the firm at ₹ 75,000. The profit for the first year after Bhim’s retirement was ₹ 1,00,000. Give the necessary journal entries to adjust Goodwill and to distribute profits showing your workings clearly.
Question 23:
(A). A, B and C were partners sharing profits in the ratio of 6 : 4 : 5. Their capitals were A – ₹ 1,00,000, B – ₹ 80,000 and C – ₹ 60,000. On 1st April 2023, B retired from the firm and the new profit sharing ratio between A and C was decided as 11 : 4. On B’s retirement the goodwill of the firm was valued at ₹ 1,80,000. Showing your calculations clearly pass necessary journal entry for the treatment of goodwill on B’s retirement.
(B). X, Y and Z were partners in a firm sharing profits in the ratio of 3 : 2 : 1. Z retired and the new profit sharing ratio between X and Y was 1 : 2. On Z’s retirement the goodwill of the firm was valued at ₹ 30,000. Pass necessary journal entry for the treatment of goodwill on Z’s retirement.
Question 24:
A, B, C and D are partners sharing profits in the ratio of 5 : 3 : 3 : 1. On the retirement of C, goodwill was valued at ₹ 3,60,000. C’s share of goodwill will be adjusted into the Capital accounts of A, B and D. Pass necessary entry for the treatment of goodwill when new profit sharing ratio is decided at 9 : 2 : 1.
Question 25:
A, B, C and D are partners sharing profits in the ratio of 4 : 3 : 2 : 1. On the retirement of B, Goodwill was valued at ₹ 3,00,000. A, C and D decide to continue the firm sharing profits equally. Pass the necessary journal entry.
Question 26:
X, Y and Z are partners sharing profits and losses in the ratio of 3 : 2 : 1. Y retires selling his share to X and Z for ₹ 1,60,000, ₹ 1,00,000 being paid by X and ₹ 60,000 by Z. The profit for the year after Y’s retirement is ₹ 2,40,000.
Pass entries to (a) record the sale of Y’s share to X and Z, and (b) distribute the profit between X and Z.
Question 27:
A, B and C were partners sharing profits and losses in the ratio of 5 : 3 : 2. Following was their Balance Sheet as at 31st March, 2023:
| Liabilities | ₹ | Assets | ₹ |
| Sundry Creditors | 1,20,000 | Cash at Bank | 34,000 |
| Capital A/cs: A B C | 4,00,000 2,50,000 1,50,000 | Sundry Debtors 1,50,000 Less: Provision for Doubtful Debts 9,000 | 1,41,000 |
| Stock | 1,45,000 | ||
| Plant | 2,00,000 | ||
| Land and Building | 4,00,000 | ||
| 9,20,000 | 9,20,000 |
A retires on this date and the following adjustments were agreed upon:
(i) Bad Debts amounting to ₹ 10,000 were to be written off and provision for doubtful debts be maintained at existing rate.
(ii) An unrecorded creditor of ₹ 20,000 will be taken into account.
(iii) Provision is to be made for legal damages amounting to ₹ 25,000.
(iv) There is a liability for ₹ 15,000 for outstanding salaries.
(v) Sundry creditors be reduced by ₹ 8,000 being a liability not payable.
(vi) Stock be increased by ₹ 15,000 and Plant is to be reduced to ₹ 1,80,000.
Pass journal entries to give effect to above adjustments and prepare Revaluation Account.
