Class 12 Accountancy Vol 1 Chapter 5 - Admission of a Partner

TS Grewal Solutions for Class 12 Accountancy Vol 1 Chapter 5

TS Grewal Solutions for Class 12 Accountancy Chapter 5 – Admission of a partner is considered to be an essential concept to be learnt completely by the students. Here, we have provided TS Grewal Accountancy solutions for class 12 in a simple and a step by step manner, which is helpful for the students to score well in their upcoming board examinations.

Chapter 5 – Admission of a partner explains the below-mentioned concepts:

• Revaluation account, cash account and balance sheet
• Calculation of ratios
• Adjustment of Capital
• Goodwill: Valuation and Treatment

TS Grewal Solutions for Class 12 Accountancy Chapter 5 – Admission of a partner

Question 1

X, Y, and Z are partners sharing profits and losses in the ratio of 5 : 3: 2. They admit A into partnership and give him 1/5th share of profits. Find the new profit-sharing ratio.

Solution:

Old Ratio = X: Y: Z = 5:3:2

1/5 share of profit is provided to A

Let assume the profit share for all partners after the admission of A is 1

So, X, Y, and Z combined share after A’s admission =1 − A’s share

= 1- \(\frac{1}{5}\) = \(\frac{4}{5}\) (this is the combined share of X, Y, and Z)

New Ratio = Old Ratio X (combined share of X, Y, and Z)

A’s share = \(\frac{5}{10}\) X \(\frac{4}{5}\) = \(\frac{20}{50}\)

Bs share = \(\frac{3}{10}\) X \(\frac{4}{5}\) = \(\frac{12}{50}\)

C’s share = \(\frac{2}{10}\) X \(\frac{4}{5}\) = \(\frac{8}{50}\)

So, the profit sharing ratio between X, Y, Z, and A will be \(\frac{20}{50}\) : \(\frac{12}{50}\) : \(\frac{8}{50}\) : \(\frac{1}{50}\) or 10 : 6: 4 :5 respectively

Question 2

Ravi and Mukesh are sharing profits in the ratio of 7 : 3. They admit Ashok for 3/7th share in the firm which he takes 2/7th from Ravi and 1/7th from Mukesh. Calculate the new profit-sharing ratio.

Solution:

The old ratio of Ravi and Mukesh is \(\frac{7}{10}\) : \(\frac{3}{10}\) \(\frac{3}{7}\) share of profit is admitted by Ashok

Ravi sacrifice \(\frac{2}{7}\) in favour of Ashok

Mukesh sacrifice \(\frac{1}{7}\) in favour of Ashok

New Ratio = Old Ratio – Sacrificing Ratio

Ravi’s Share = \(\frac{7}{10}\) – \(\frac{2}{7}\) = \(\frac{29}{70}\)

Mukesh’s share = \(\frac{3}{10}\) – \(\frac{1}{7}\) = \(\frac{11}{70}\)

So, the new profit sharing ratio between Ravi, Mukesh, and Ashok will be,

Ravi \(\frac{29}{70}\) : Mukesh \(\frac{11}{70}\) : Ashok \(\frac{3}{7}\) = \(\frac{29:11:3}{70}\) = 29:11:3

Question 3

A and B are partners sharing profits and losses in the proportion of 7 : 5. They agree to admit C, their manager, into partnership who is to get 1/6th share in the profits. He acquires this share as 1/24th from A and 1/8th from B. Calculate new profit-sharing ratio.

Solution:

The old ratio of A and B = 7:5

A sacrifice \(\frac{1}{24}\) in favour of C

B sacrifice \(\frac{1}{8}\) in favour of C

New Ratio = Old Ratio – Sacrificing Ratio

As Share = \(\frac{7}{12}\) – \(\frac{1}{24}\) = \(\frac{13}{24}\)

B’s share = \(\frac{5}{12}\) – \(\frac{1}{8}\) = \(\frac{7}{24}\)

So, the new profit sharing ratio between A, B, and C will be = \(\frac{13}{24}\) : \(\frac{7}{24}\) : \(\frac{1}{6}\) = \(\frac{13:7:4}{24}\) = 13:7:4

Question 4

A, B and C were partners in a firm sharing profits in the ratio of 3 : 2 : 1. They admitted D as a new partner for 1/8th share in the profits, which he acquired 1/16th from B and 1/16th from C. Calculate the new profit-sharing ratio of A, B, C and D.

Solution:

The profit-sharing ratio of A, B, and C = 3:2:1

Original share of A = \(\frac{3}{6}\)

D’s share = \(\frac{1}{8}\) (out of which \(\frac{1}{6}\) is acquired from B and C each

New share of B = \(\frac{2}{6}\) – \(\frac{1}{16}\) = \(\frac{13}{48}\)

New share of C = \(\frac{1}{6}\) – \(\frac{1}{16}\) = \(\frac{5}{48}\)

So, the new profit sharing ratio between A, B, C, and D is = \(\frac{3}{6}\) : \(\frac{13}{48}\) : \(\frac{5}{48}\) : \(\frac{1}{8}\) = \(\frac{24:13:5:6}{48}\) = 24:13:5:6

Question 5

Bharati and Astha were partners sharing profits in the ratio of 3 : 2. They admitted Dinkar as a new partner for 1/5th share in the future profits of the firm which he got equally from Bharati and Astha. Calculate the new profit-sharing ratio of Bharati, Astha and Dinkar.

Solution:

The old ratio of Bharati and Astha = 3:2

Dinkar share = \(\frac{1}{5}\)

Bharati sacrifices = \(\frac{1}{5}\) X \(\frac{1}{2}\) = \(\frac{1}{10}\)

Astha sacrifices = \(\frac{1}{5}\) X \(\frac{1}{2}\) = \(\frac{1}{10}\)

Bharati’s New Share = \(\frac{3}{5}\) – \(\frac{1}{10}\) = \(\frac{6-1}{10}\) = \(\frac{5}{10}\)

Astha’s New share = \(\frac{2}{5}\) – \(\frac{1}{10}\) = \(\frac{4-1}{10}\) = \(\frac{3}{10}\)

Dinkar’s New share = \(\frac{1}{5}\) X \(\frac{2}{2}\) = \(\frac{2}{10}\)

So, Bharati : Astha : Dinkar = 5 : 3 : 2

Question 6

X and Y are partners in a firm sharing profits and losses in the ratio of 3 : 2. Z is admitted as a partner with 1/4 share in profit. Z acquires his share from X and Y in the ratio of 2 : 1. Calculate new profit-sharing ratio.

Solution:

The old ratio of X and Y = 3:2

Sacrificing ratio of X and Y is 2:1

Z acquired share from X = \(\frac{2}{3}\) X \(\frac{1}{4}\) = \(\frac{2}{12}\)

Z acquired share from Y = \(\frac{1}{3}\) X \(\frac{1}{4}\) = \(\frac{2}{12}\)

New Ratio = Old ratio – Sacrificing ratio

X’s New Share = \(\frac{3}{5}\) – \(\frac{2}{12}\) = \(\frac{36-10}{60}\) = \(\frac{26}{60}\)

Y’s New share = \(\frac{2}{5}\) – \(\frac{1}{2}\) = \(\frac{24-5}{60}\) = \(\frac{19}{60}\)

Z’s New share = \(\frac{1}{4}\) X \(\frac{15}{15}\) = \(\frac{15}{60}\)

So, X : Y : Z = 26 : 19 : 15

Question 7

R and S are partners sharing profits in the ratio of 5 : 3. T joins the firm as a new partner. R gives 1/4th of his share and S gives 1/5th of his share to the new partner. Find out new profit-sharing ratio.

Solution:

The old ratio of R and S = 5 : 3

Sacrificing ratio = Old Ratio X Surrender Ratio

Sacrificing ratio of R and = \(\frac{5}{8}\) X \(\frac{1}{4}\) = \(\frac{5}{32}\)

Sacrificing ratio of S and = \(\frac{3}{8}\) X \(\frac{1}{5}\) = \(\frac{3}{40}\)

New Ratio = Old Ratio – Sacrificing Ratio

R’s New Share = \(\frac{5}{8}\) – \(\frac{5}{32}\) = \(\frac{15}{32}\)

S’s New share = \(\frac{3}{8}\) – \(\frac{3}{40}\) = \(\frac{15}{32}\)

T’s Share = R’s sacrifice + S’s sacrifice

T’s Share = \(\frac{5}{32}\) + \(\frac{3}{40}\) = \(\frac{25+12}{160}\) = \(\frac{37}{160}\)

New profit sharing ratio between R, S, and T = \(\frac{15}{32}\) : \(\frac{15}{32}\) : \(\frac{37}{160}\) = \(\frac{75:48:37}{160}\) or 75 : 48 : 37

Question 8

Kabir and Farid are partners in a firm sharing profits and losses in the ratio of 7 : 3. Kabir surrenders 2/10th from his share and Farid surrenders 1/10th from his share in favour of Jyoti; the new partner. Calculate new profit-sharing ratio and sacrificing ratio.

Solution:

The old ratio of Kabir : Farid = 7:5

Kabir sacrifice \(\frac{2}{10}\) in favour of Jyoti

Farid sacrifice \(\frac{1}{10}\) in favour of Jyoti

Jyoti’s share = \(\frac{2}{10}\) + \(\frac{1}{10}\) = \(\frac{3}{10}\)

New Ratio = Old Ratio – Sacrificing Ratio

Kabir’s New Share = \(\frac{7}{10}\) – \(\frac{2}{10}\) = \(\frac{5}{10}\)

Farid’s New share = \(\frac{3}{10}\) – \(\frac{1}{10}\) = \(\frac{2}{10}\)

So, the new profit sharing ratio between Kabir, Farid, and Jyoti will be = 5 : 2 : 3

The Sacrificing ratio of Kabir and Farid is \(\frac{2}{10}\) and \(\frac{1}{10}\) = 2:1

Question 9

Find New Profit-sharing Ratio:

(i) R and T are partners in a firm sharing profits in the ratio of 3 : 2. S joins the firm. R surrenders 1/4th of his share and T 1/5th of his share in favour of S.

(ii) A and B are partners. They admit C for 1/4th share. In the future, the ratio between A and B would be 2 : 1.

(iii) A and B are partners sharing profits and losses in the ratio of 3 : 2. They admit C for 1/5th share in the profit. C acquires 1/5th of his share from A and 4/5th share from B.

(iv) X, Y and Z are partners in the ratio of 3 : 2 : 1. W joins the firm as a new partner for 1/6th share in profits. Z would retain his original share.

(v) A and B are equal partners. They admit C and D as partners with 1/5th and 1/6th share respectively.

(vi) A and B are partners sharing profits/losses in the ratio of 3 : 2 . C is admitted for 1/4th share. A and B decide to share equally in future.

Solution:

(i) The old ratio of R : T = 7:5

Sacrificing ratio = Old ratio X Surrender ratio

R’s Sacrificing Share = \(\frac{3}{5}\) X \(\frac{1}{4}\) = \(\frac{3}{20}\)

T’s Sacrificing Share = \(\frac{2}{5}\) X \(\frac{1}{5}\) = \(\frac{2}{25}\)

New Ratio = Old Ratio – Sacrificing Ratio

R’s New Share = \(\frac{3}{5}\) – \(\frac{3}{20}\) = \(\frac{9}{20}\)

T’s New share = \(\frac{2}{5}\) – \(\frac{2}{25}\) = \(\frac{8}{25}\)

S’s share = R’s sacrificing share + T’s sacrificing share

= \(\frac{3}{20}\) + \(\frac{2}{25}\) = \(\frac{23}{100}\)

So, the new profit sharing ratio between R, T, and S will be = \(\frac{9}{20}\) : \(\frac{8}{25}\) : \(\frac{23}{100}\) = \(\frac{45: 32 : 23}{100}\) or 45: 32 : 23

(ii) The old ratio of A : B = 1 : 1

Combined share of A and B = 1- C‘s share = 1- \(\frac{1}{4}\) = \(\frac{3}{4}\)

New ratio = Combined share of A and B X \(\frac{2}{3}\)

A’s New Share = \(\frac{3}{4}\) X \(\frac{2}{3}\) = \(\frac{6}{12}\)

B’s New share = \(\frac{3}{4}\) X \(\frac{1}{3}\) = \(\frac{3}{12}\)

New Profit sharing ratio A : B : C = \(\frac{6}{12}\) : \(\frac{3}{12}\) : \(\frac{1}{4}\) = \(\frac{6: 3 : 3}{100}\) = 2 : 1 :1

(iii) The old ratio of A : B = 3 : 2

A’s sacrifice = C’s share X \(\frac{1}{5}\)

= \(\frac{1}{5}\) X \(\frac{1}{5}\) = \(\frac{1}{25}\)

B’s sacrifices= C’s share X \(\frac{4}{5}\)

= \(\frac{1}{5}\) X \(\frac{4}{5}\) = \(\frac{4}{25}\)

New Ratio = Old Ratio – Sacrificing Ratio

A’s share = \(\frac{3}{5}\) – \(\frac{1}{25}\) = \(\frac{15-1}{25}\)= \(\frac{14}{25}\)

B’s share = \(\frac{2}{5}\) – \(\frac{4}{25}\) = \(\frac{10-4}{25}\) = \(\frac{6}{25}\)

New Profit Sharing Ratio = A : B : C = \(\frac{14}{25}\) : \(\frac{6}{25}\) : \(\frac{1}{5}\) = \(\frac{14 : 6 : 1}{25}\) = 14 : 6 : 1

(iv) The old ratio of X : Y : Z = 3 : 2 : 1

After admitting W and combining all the partner’s share , let the share be = 1

X and Y combined share in the new firm = 1 – Z’s share – W’s share

= 1 – \(\frac{1}{6}\) – \(\frac{1}{6}\) = \(\frac{4}{6}\)

New Ratio = Old Ratio X combined share of X and Y

X’s share = \(\frac{3}{5}\) X \(\frac{4}{6}\) = \(\frac{12}{30}\)

Y’s share = \(\frac{2}{5}\) X \(\frac{4}{6}\) = \(\frac{8}{30}\)

New Profit Sharing Ratio = X : Y : Z : W = \(\frac{12}{30}\) : \(\frac{8}{30}\) : \(\frac{1}{6}\) : \(\frac{1}{6}\) = \(\frac{12 : 8 : 5 : 5}{30}\) or 12 : 8 : 5 : 5

(v) The old ratio of A : B = 1:1

After admitting C and D and combining all the partner’s share , let the share be = 1

Combined share of profit of A and B after C and D’s admission = 1 – C’s share – D’s share

A and B combined share after C and D’s admission = 1 – Z’s share – W’s share

= 1 – \(\frac{1}{5}\) – \(\frac{1}{6}\) = \(\frac{19}{30}\)

New Ratio = Old Ratio X combined share of A and B

A’s share = \(\frac{1}{2}\) X \(\frac{19}{30}\) = \(\frac{19}{60}\)

B’s share = \(\frac{1}{2}\) X \(\frac{19}{30}\) = \(\frac{19}{60}\)

New Profit Sharing Ratio = A : B : C : D = \(\frac{19}{60}\) : \(\frac{19}{60}\) : \(\frac{1}{5}\) : \(\frac{1}{6}\) = \(\frac{19 : 19 : 12 : 10}{60}\) or 19 : 19 : 12 : 10

(vi) The old ratio of A : B = 3 : 2

After admitting C and combining all the partner’s share , let the share be = 1

Combined share of profit of A and B after D’s admission = 1 – C’s share

= 1 – \(\frac{1}{4}\) = \(\frac{3}{4}\)

A and B New Ratio = combined share of A and B X \(\frac{1}{2}\)

A and B New Ratio = \(\frac{3}{4}\) X \(\frac{1}{2}\) = \(\frac{3}{8}\)

New Profit Sharing Ratio = A : B : C = \(\frac{3}{8}\) : \(\frac{3}{8}\) : \(\frac{1}{4}\) = \(\frac{3 : 3 : 2}{8}\) or 3 : 3 : 2

Question 10

X and Y were partners sharing profits in the ratio of 3 : 2. They admitted P and Q as new partners. X surrendered 1/3rd of his share in favour of P and Y surrendered 1/4th of his share in favour of Q. Calculate new profit-sharing ratio of X, Y, P and Q.

Solution:

The old ratio of X : Y = 3 : 2

Sacrificing ratio = Old ratio X Surrender ratio

X’s Sacrificing Share = \(\frac{3}{5}\) X \(\frac{1}{3}\) = \(\frac{3}{15}\)

Y’s Sacrificing Share = \(\frac{2}{5}\) X \(\frac{1}{4}\) = \(\frac{2}{20}\)

New Ratio = Old Ratio – Sacrificing Ratio

X’s share = \(\frac{3}{5}\) – \(\frac{3}{15}\) = \(\frac{6}{15}\)

Y’s share = \(\frac{2}{5}\) – \(\frac{2}{20}\) = \(\frac{6}{20}\)

X sacrificed for P = \(\frac{3}{15}\)

Y sacrificed for Q = \(\frac{2}{10}\)

So, the profit sharing ratio between X, Y, P, and Q will be \(\frac{6}{15}\) : \(\frac{6}{20}\) : \(\frac{3}{15}\) : \(\frac{2}{10}\) = \(\frac{24 : 8 : 12 : 6}{60}\) or 10 : 6: 4 :5 respectively

Question 11

Rakesh and Suresh are sharing profits in the ratio of 4 : 3. Zaheer joins and the new ratio among Rakesh, Suresh and Zaheer is 7 : 4 : 3. Find out the sacrificing ratio.

Solution:

The old ratio of Rakesh : Suresh = 4 : 3

New ratio for Rakesh, Suresh and Zaheer = 7 : 4 : 3

Sacrificing ratio = Old ratio – New ratio

Rakesh’s Share = \(\frac{4}{7}\) – \(\frac{7}{14}\) = \(\frac{1}{14}\)

Suresh’s Share = \(\frac{3}{7}\) – \(\frac{4}{14}\) = \(\frac{2}{14}\)

So, sacrificing ratio of Rakesh and Suresh = \(\frac{1}{14}\) : \(\frac{2}{14}\) = 1 : 2

Question 12

A and B are partners sharing profits in the ratio of 3 : 2. C is admitted as a partner. The new profit-sharing ratio among A, B and C is 4 : 3 : 2. Find out the sacrificing ratio.

Solution:

The old ratio A : B = 3 : 2

New ratio for A, B and C = 4 : 3 : 2

Sacrificing ratio = Old ratio – New ratio

A’s Share = \(\frac{3}{5}\) – \(\frac{4}{9}\) = \(\frac{7}{45}\)

B’s Share = \(\frac{2}{5}\) – \(\frac{3}{9}\) = \(\frac{3}{45}\)

So, sacrificing ratio of A and B = \(\frac{7}{45}\) : \(\frac{3}{45}\) = 1 : 2

Question 13

A, B and C are partners sharing profits in the ratio of 4 : 3 : 2. D is admitted for 1/3rd share in future profits. What is the sacrificing ratio?

Solution:

Old Ratio = A : B : C = 4 : 3 : 2

Let A, B, C, and D combined share be 1

So, A, B, and C combined share after D’s admission =1 − D’s share

= 1- \(\frac{1}{3}\) = \(\frac{2}{3}\)

New Ratio = Old Ratio X (combined share of A, B, and C)

A’s share = \(\frac{4}{9}\) X \(\frac{2}{3}\) = \(\frac{8}{27}\)

Bs share = \(\frac{3}{9}\) X \(\frac{2}{3}\) = \(\frac{6}{27}\)

C’s share = \(\frac{2}{9}\) X \(\frac{2}{3}\) = \(\frac{4}{27}\)

Sacrificing ratio = Old ratio – New ratio

A’s share = \(\frac{4}{9}\) – \(\frac{8}{27}\) = \(\frac{4}{27}\)

B’s share = \(\frac{3}{9}\) – \(\frac{6}{27}\) = \(\frac{3}{27}\)

C’s share = \(\frac{2}{7}\) – \(\frac{4}{27}\) = \(\frac{2}{27}\)

So, sacrificing ratio of A : B : C will be \(\frac{4}{27}\) : \(\frac{3}{27}\) : \(\frac{2}{27}\) or 4 : 3 :2

Question 14

A, B, C and D are in partnership sharing profits and losses in the ratio of 36 : 24 : 20 : 20 respectively. E joins the partnership for 20% share and A, B, C and D in future would share profits among themselves as 3/10 : 4/10 : 2/10 : 1/10. Calculate new profit-sharing ratio after E’s admission .

Solution:

Old Ratio = A : B : C : D = 36 : 24 : 20 : 20

Let A, B, C, and D combined share be 1

So, A, B, C, and D combined share after E’s admission =1 − E’s share

= 1- \(\frac{20}{100}\) = \(\frac{80}{100}\)

New Ratio = Combined share of A, B, C, and D X Agreed share of A, B, C, and D

A’s share = \(\frac{80}{100}\) X \(\frac{3}{10}\) = \(\frac{24}{100}\)

B’s share = \(\frac{80}{100}\) X \(\frac{4}{10}\) = \(\frac{32}{100}\)

C’s share = \(\frac{80}{100}\) X \(\frac{2}{10}\) = \(\frac{16}{100}\)

D’s share = \(\frac{80}{100}\) X \(\frac{1}{10}\) = \(\frac{8}{100}\)

New sacrificing ratio of A : B : C : D : E = \(\frac{24}{100}\) : \(\frac{32}{100}\) : \(\frac{16}{100}\) : \(\frac{8}{100}\) : \(\frac{20}{100}\) = 6 : 8 : 4 : 2 : 5

Question 15

X and Y are partners sharing profits and losses in the ratio of 3 : 2. They admit Z into partnership. X gives 1/3rd of his share while Y gives 1/10th from his share to Z. Calculate new profit-sharing ratio and sacrificing ratio.

Solution:

Old Ratio = X : Y = 3 : 2

X’s sacrificing share = \(\frac{1}{3}\) X \(\frac{3}{5}\) = \(\frac{3}{15}\)

Y’s sacrificing share = \(\frac{1}{10}\)

Sacrificing ratio = \(\frac{3}{15}\) : \(\frac{1}{10}\) or 2 : 1

New share = Old Share – Sacrificed Share

X’s share = \(\frac{3}{5}\) – \(\frac{3}{15}\) = \(\frac{6}{15}\)

Y’s share = \(\frac{2}{5}\) – \(\frac{1}{10}\) = \(\frac{3}{10}\)

Z’s share = \(\frac{3}{15}\) – \(\frac{1}{10}\) = \(\frac{9}{30}\)

New Ratio = \(\frac{6}{15}\) : \(\frac{3}{10}\) : \(\frac{9}{30}\) = 4 : 3 : 3

Question 16

A, B and C are partners sharing profits in the ratio of 2 : 2 : 1. D is admitted as a new partner for 1/6th share. C will retain his original share. Calculate the new profit-sharing ratio and sacrificing ratio.

Solution:

New Profit Sharing Ratio Evaluation

Old Ratio = A : B : C = 2 : 2 : 1

E admitted \(\frac{1}{6}\)th share and C retained his share \(\frac{1}{5}\)

Remaining Share = 1- \(\frac{1}{6}\) – \(\frac{1}{5}\) = \(\frac{30-5-6}{30}\) = \(\frac{19}{30}\)

A and B will share the other ratio in 2 : 2 old ratio

A’s new share = \(\frac{19}{30}\) X \(\frac{2}{4}\) = \(\frac{38}{120}\)

B’s new share = \(\frac{19}{30}\) X \(\frac{2}{4}\) = \(\frac{28}{120}\)

C’s new share = \(\frac{1}{5}\) X \(\frac{24}{24}\) = \(\frac{24}{120}\)

D’s new share = \(\frac{1}{6}\) X \(\frac{20}{20}\) = \(\frac{20}{120}\)

Since, the sacrificed ratio is not mentioned it is assumed that A and B sacrificed their share is their old ratio

Sacrificing ratio = Old ratio – New ratio

A’s share = \(\frac{2}{5}\) – \(\frac{19}{60}\) = \(\frac{24-19}{60}\) = \(\frac{5}{60}\)

B’s share = \(\frac{2}{5}\) – \(\frac{19}{60}\) = \(\frac{24-19}{60}\) = \(\frac{5}{60}\)

So, sacrificing ratio of A : B : C is 5 : 5 or 1 : 1

Question 17

A and B are in partnership sharing profits and losses as 3 : 2. C is admitted for 1/4th share. Afterwards D enters for 20 paise in the rupee. Compute profit-sharing ratio of A, B, C and D after D’s admission.

Solution:

Old Ratio = A : B = 3 : 2

C admitted \(\frac{1}{6}\)th profit share

Let A, B, C, and D combined share be 1

So, A, B, C, and D combined share after E’s admission =1 − E’s share

= 1- \(\frac{1}{4}\) = \(\frac{3}{4}\)

New Ratio = Old ratio X combined share of A and B

A’s share = \(\frac{3}{5}\) X \(\frac{3}{4}\) = \(\frac{9}{20}\)

B’s share = \(\frac{2}{5}\) X \(\frac{3}{4}\) = \(\frac{6}{20}\)

New profit sharing ratio after admission of C = A : B : C = \(\frac{9}{20}\) : \(\frac{6}{20}\) : \(\frac{1}{4}\) = \(\frac{9 : 6 : 5}{20}\) or 9 : 6 : 5

After C’s admission the profit sharing ratio will become old ratio when determining the new profit ratio after D’s admission

Ratio before admission of D = A : B : C = 9 : 6 : 5

D admitted \(\frac{20}{100}\)th profit share

Let combines share of A, B, and C, after Ds admission be 1

So, A, B, and C combined share after D’s admission =1 − D’s share

= 1- \(\frac{20}{100}\) = \(\frac{80}{100}\)

New Ratio = Old ratio X combined share of A, B, and C

A’s share = \(\frac{9}{20}\) X \(\frac{80}{100}\) = \(\frac{72}{200}\)

B’s share = \(\frac{6}{20}\) X \(\frac{80}{100}\) = \(\frac{48}{200}\)

C’s share = \(\frac{5}{20}\) X \(\frac{80}{100}\) = \(\frac{40}{200}\)

So, new profit sharing ratio between A : B : C : D will be \(\frac{72}{200}\) : \(\frac{48}{200}\) : \(\frac{40}{200}\) : \(\frac{20}{100}\) = 9 : 6 : 5 : 5

Question 18

P and Q are partners sharing profits in the ratio of 3 : 2. They admit R into partnership who acquires 1/5th of his share from P and 4/25th share from Q. Calculate New Profit-sharing Ratio and Sacrificing Ratio.

Solution:

Old Ratio P : Q = 3 : 2

Remaining share of P\(\frac{4}{5}\)(1-\(\frac{1}{5}\) )of his share from Q

If R share \(\frac{4}{5}\) = \(\frac{1}{25}\)

P’s share = \(\frac{1}{5}\) X \(\frac{1}{5}\) = \(\frac{1}{25}\)

Q’s share = \(\frac{4}{25}\)

P’s new share = \(\frac{3}{5}\) – \(\frac{1}{25}\) = \(\frac{15-1}{25}\) = \(\frac{14}{25}\)

Q’s new share = \(\frac{2}{5}\) – \(\frac{4}{25}\) = \(\frac{10-4}{25}\) = \(\frac{6}{25}\)

R’s new share = \(\frac{1}{5}\) X \(\frac{5}{5}\) = \(\frac{5}{25}\)

New Share P : Q : R = 14 : 6 :5

Sacrificing ratio = 1 : 4

Question 19

A and B are partners sharing profits and losses in the ratio of 2 : 1. They take C as a partner for 1/5th share. Goodwill Account appears in the books at ₹ 15,000. For the purpose of C’s admission, goodwill of the firm is valued at ₹ 15,000. C is to pay a proportionate amount as premium for goodwill which he pays to A and B privately.

Pass necessary entries.

Solution:

Note- The goodwill brought by C will not be recorded in the journal books as the amount is paid privately to A and B.

Working Note: Goodwill Written-off Evaluation

Debited A’s capital = 15,000 X \(\frac{2}{3}\) = ₹ 10,000

Credited B’s capital = 15,000 X \(\frac{1}{3}\) = ₹ 5,000

Question 20

A and B are partners sharing profits and losses in the ratio of 2 : 5. They admit C on the condition that he will bring ₹ 14,000 as his share of goodwill to be distributed between A and B. C’s share in the future profits or losses will be 1/4th. What will be the new profit-sharing ratio and what amount of goodwill brought in by C will be received by A and B?

Solution:

Old ratio A : B = 2 : 5

C admitted \(\frac{1}{4}\)th profit share

Let A, B, and C combined share be 1

A and B combined share after C’s admission = 1 – C’s share

1- \(\frac{1}{4}\) = \(\frac{3}{4}\)

New ratio = Old ratio X combined share of A and B

A’s share= \(\frac{2}{7}\) X \(\frac{3}{4}\) = \(\frac{6}{28}\)

B’s share= \(\frac{5}{7}\) X \(\frac{3}{4}\) = \(\frac{15}{28}\)

New Profit Sharing Ratio = A : B : C = \(\frac{6}{28}\) : \(\frac{15}{28}\) : \(\frac{1}{4}\) = \(\frac{6 : 15 : 7}{28}\) = 6 : 15 : 7

C’s Goodwill share distribution

C’s goodwill share = ₹ 14,000

A will receive = 14,000 X \(\frac{2}{7}\) = ₹ 4,000

B will receive = 14,000 X \(\frac{5}{7}\) = ₹ 10,000

Question 21

A and B are partners in a firm sharing profits and losses in the ratio of 3 : 2. A new partner C is admitted. A surrenders 1/5th of his share and B surrenders 2/5th of his share and B surrenders 2/5th of his share in favour of C. For the purpose of C’s admission, goodwill of the firm is valued at ₹ 75,000 and C brings in his share of goodwill in cash which is retained in the firm’s books. Journalise the above transactions.

Solution:

Old ratio A : B = 3 : 2

A sacrifices = \(\frac{3}{5}\) X \(\frac{1}{5}\) = \(\frac{3}{25}\)

B sacrifices = \(\frac{2}{5}\) X \(\frac{2}{5}\) = \(\frac{4}{25}\)

Sacrificing ratio of A : B = \(\frac{3}{25}\) : \(\frac{4}{25}\) = 3 : 4

New ratio – Old ratio – Sacrificing ratio

A’s new ratio share = \(\frac{3}{5}\) – \(\frac{3}{25}\) = \(\frac{12}{25}\)

B’s new ratio share = \(\frac{2}{5}\) – \(\frac{4}{25}\) = \(\frac{6}{25}\)

C’s new ratio share = A sacrifice + B sacrifice = \(\frac{3}{25}\) + \(\frac{4}{25}\) = \(\frac{7}{25}\)

So, New ratio A : B : C = 12 : 6 : 7

Goodwill premium bought by C= 75,000 X \(\frac{7}{25}\) = 21, 000

Goodwill premium distribution

Goodwill of A = 21,000 X \(\frac{3}{7}\) = 9, 000

Goodwill of B = 21,000 X \(\frac{4}{7}\) = 12, 000

Question 22

Give Journal entries to record the following arrangements in the books of the firm:

(a) B and C are partners sharing profits in the ratio of 3 : 2. D is admitted paying a premium (goodwill) of ₹ 2,000 for 1/4th share of the profits, shares shares of B and C remain as before.

(b) B and C are partners sharing profits in the ratio of 3 : 2. D is admitted paying a premium of ₹ 2,100 for 1/4th share of profits which he acquires 1/6th from B and 1/12th from C.

Solution:

(a)

Working Note: Distribution of goodwill premium

Goodwill of B = 2,000 X \(\frac{3}{5}\) = 1,200

Goodwill of C = 2,000 X \(\frac{2}{5}\) = 800

(b)

Working Note 1 : Distribution of goodwill premium

Sacrificing ratio = B : C = latex]\frac{1}{6}\) : latex]\frac{1}{12}\) = 2 : 1

Working Note 2 : Distribution of goodwill premium

Goodwill of B = 2,100 X \(\frac{2}{3}\) = 1,400

Goodwill of C = 2,100 X \(\frac{1}{5}\) = 700

Question 23

B and C are in partnership sharing profits and losses as 3 : 1. They admited D into the firm, D pays premium of ₹ 15,000 for 1/3rd share of the profits. As between themselves, B and C agree to share future profits and losses equally. Draft Journal entries showing appropriations of the premium money.

Solution:

Working Notes 1: Sacrificing Ratio Evaluation

Let B and C combined share after D’s be 1

B and C combined share after D’s admission = 1 – D’s share

1- \(\frac{1}{3}\) = \(\frac{2}{3}\)

Profit sharing of B and C after D’s admission = \(\frac{2}{3}\) X \(\frac{1}{2}\) = \(\frac{1}{3}\) each

Sacrificing ratio = New ratio – New ratio

B’s share = \(\frac{3}{4}\) – \(\frac{1}{3}\) = \(\frac{5}{12}\) (sacrificing)

C’s share = \(\frac{1}{4}\) – \(\frac{1}{3}\) = \(\frac{-1}{12}\) (gain)

Working Notes 2:

C gains in the new firm. So, C’s goodwill gain will be debited from his capital A/c and given to the sacrificing partner B.

Firm’s goodwill = Goodwill premium brought by D X Reciprocal of D’s share

= 15,000 X \(\frac{3}{1}\) = ₹ 45,000

C’s share of Goodwill gain = Firm goodwill X Share of gain

= 45,000 X \(\frac{1}{12}\) = ₹ 3,750

Question 24

M and J are partners in a firm sharing profits in the ratio of 3 : 2. They admit R as a new partner. The new profit-sharing ratio between M, J and R will be 5 : 3 : 2. R brought in ₹ 25,000 for his share of premium for goodwill. Pass necessary Journal entries for the treatment of goodwill.

Solution:

Working Notes 1: Sacrificing Ratio Evaluation

Sacrificing ratio = Old ratio – New ratio

M’s sacrificing ratio = \(\frac{3}{5}\) – \(\frac{5}{10}\) = \(\frac{1}{10}\)

J’s sacrificing ratio = \(\frac{2}{5}\) – \(\frac{3}{10}\) = \(\frac{1}{10}\)

Sacrificing ratio = M : J = \(\frac{1}{10}\) : \(\frac{1}{10}\) = 1 : 1

Working Notes 2: R’s goodwill share Evaluation

M’s goodwill share = 25,000 X \(\frac{1}{2}\) = ₹ 12,500

J’s goodwill share = 25,000 X \(\frac{1}{2}\) = ₹ 12,500

So, M and N will receive 12,500 each

Question 25

A and B are in partnership sharing profits and losses in the ratio of 5 : 3. C is admitted as a partner who pays ₹ 40,000 as capital and the necessary amount of goodwill which is valued at ₹ 60,000 for the firm. His share of profits will be 1/5th which he takes 1/10th from A and 1/10th from B.

Give Journal entries and also calculate future profit-sharing ratio of the partners.

Solution:

Working Notes 1 : A and B Sacrificing Ratio

A : B = \(\frac{1}{10}\) : \(\frac{1}{10}\) = 1 : 1

Working Notes 2 : New Profit Sharing Ratio Evaluation

Old ratio of A : B = 5 : 3

New ratio = Old ratio – Sacrificing ratio

A’s share = \(\frac{5}{8}\) – \(\frac{1}{10}\) = \(\frac{21}{40}\)

B’s share = \(\frac{3}{8}\) – \(\frac{1}{10}\) = \(\frac{11}{40}\)

New Profit Sharing Ratio = A : B : C = \(\frac{21}{40}\) : \(\frac{11}{40}\) : \(\frac{1}{5}\) = \(\frac{21 : 11: 8}{40}\)

Working Notes 3 : Distribution of R’s goodwill share Evaluation

A’s goodwill share = 12,000 X \(\frac{1}{2}\) = ₹ 6,000

B’s goodwill share = 12,000 X \(\frac{1}{2}\) = ₹ 6,000

So, A and B will receive 6,000 each

Also Check: Important Questions for Admission of a partner
The above-provided solutions are considered to be the best solutions for ‘TS Grewal Solutions Class 12 Accountancy Vol 1 Chapter 5- Admission of a partner’. Stay tuned to BYJU’S to learn more and score well in the upcoming board examinations.