 # 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.

 Board CBSE Class Class 12 Subject Accountancy Chapter Chapter 5 Chapter Name Admission of a partner Number of questions solved 06 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)

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

$\frac{1}{6}$ 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 Entry Date Particulars L.F. Debit ₹ Credit ₹ A’s Capital A/c Dr. 10,000 B’s Capital A/c Dr. 5,000 To Goodwill A/c 15,000 (Goodwill written-off between A and B in the old ratio of 2:1)

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. 52,000 To C’s Capital A/c 40,000 To Premium for Goodwill A/c 12,000 (Being goodwill share and capital bought by C in cash) Premium for Goodwill A/c Dr. 12,000 To A’s Capital A/c 6,000 To B’s Capital A/c 6,000 (Being C’s goodwill share distributed between A and B)

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.

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