 # TS Grewal Solutions Class 12 Accountancy Vol 1 Chapter 5 - Admission of a Partner

## TS Grewal Solutions Class 12 Accountancy Vol 1 Chapter 5

TS Grewal Accountancy Class 12 Solutions 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.

 Board CBSE Class Class 12 Subject Accountancy Chapter Chapter 5 Chapter Name Admission of a partner Number of questions solved 25 Category TS Grewal

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

• Revaluation account, cash account and balance sheet
• Calculation of ratios
• 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)

X’s share = $$\frac{5}{10}$$ X $$\frac{4}{5}$$ = $$\frac{20}{50}$$

Ys share = $$\frac{3}{10}$$ X $$\frac{4}{5}$$ = $$\frac{12}{50}$$

Z’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

$$\frac{1}{6}$$ share of profit is admitted by C

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

$$\frac{1}{4}$$th share of profit is admitted by Z

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

$$\frac{1}{4}$$th profit share is admitted by C

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

$$\frac{1}{5}$$th profit share is admitted by C

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

$$\frac{1}{6}$$th profit share is admitted by W

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

$$\frac{1}{5}$$th profit share is admitted by C

$$\frac{1}{6}$$th profit share is admitted by D

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

$$\frac{1}{4}$$th profit share is admitted by C

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

$$\frac{1}{3}$$th profit share is admitted by D

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

$$\frac{20}{100}$$th profit share is admitted by E

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

$$\frac{1}{5}$$ of P’s share is acquired by R

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:

Journal

 Date Particulars L.F. Debit (₹) Credit (₹) A’s Capital A/c                 Dr. B’s Capital A/c                 Dr. To Goodwill A/c (Goodwill written-off between A and B in the old ratio of 2:1) 10,000 5,000 15,000

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:

 Date Particulars L.F. Debit ₹ Credit ₹ Cash A/c Dr. 21,000 To Premium for Goodwill A/c 21,000 (Premium Goodwill brought by C) Premium for Goodwill A/c Dr. 21,000 To A’s Capital A/c 9,000 To B’s Capital A/c 12,000 (Distributed Goodwill Premium brought by C between A and B in sacrificing ratio 3:4)

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 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)

 Journal Date Particulars L.F. Debit ₹ Credit ₹ Cash A/c Dr. 2,000 To Premium for Goodwill A/c 2,000 (Goodwill Premium brought by D) Premium for Goodwill A/c Dr. 2,000 To B’s Capital A/c 1,200 To C’s Capital A/c 800 (Distributed Goodwill Premium between B and C in sacrificing ratio 3:2)

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)

 Journal Date Particulars L.F. Debit ₹ Credit ₹ Cash A/c Dr. 2,100 To Premium for Goodwill A/c 2,100 (Goodwill share bought by D in cash) Premium for Goodwill A/c Dr. 2,100 To B’s Capital A/c 1,400 To C’s Capital A/c 700 (Distributed Goodwill Premium between B and C in sacrificing Ratio 2:1)

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:

 Journal Date Particulars L.F. Debit ₹ Credit ₹ Cash A/c Dr. 15,000 To Premium for Goodwill A/c 15,000 (Goodwill share bought by D in cash) Premium for Goodwill A/c Dr. 15,000 To B’s Capital A/c 15,000 (Goodwill premium transferred to B’s Capital) C’s Capital A/c Dr. 3,750 To B’s Capital A/c 3,750 (Being charges goodwill from C’s capital A/c due to his gain in profit sharing)

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:

 Journal Date Particulars L.F. Debit ₹ Credit ₹ Cash A/c Dr. 25,000 To Premium for Goodwill A/c 25,000 (Goodwill share bought by C in cash) Premium for Goodwill A/c Dr. 25,000 To M’s Capital A/c 12,500 To J’s Capital A/c 12,500 (Distributed C’s Goodwill share between M and J in their sacrificing ratio)

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:

Journal

 Date Particulars L.F. Debit (₹) Credit (₹) Cash A/c                                         Dr. To C’s Capital A/c To Premium for Goodwill A/c (Goodwill share and capital bought by C in cash) 52,000 40,000 12,000 Premium for Goodwill A/c           Dr. To A’s Capital A/c To B’s Capital A/c (C’s goodwill share distributed between A and B) 12,000 6,000 6,000

A : B = $$\frac{1}{10}$$ : $$\frac{1}{10}$$ = 1 : 1

Working Notes 1 : A and B Sacrificing Ratio

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

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.

 Important Topics in Accountancy: What is a Balance Sheet? Partnership Deed What is Goodwill? Treatment of Goodwill What Is Partnership

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