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 belowmentioned 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 profitsharing 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 Aâ€™s admission =1 âˆ’ Aâ€™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)
Aâ€™s share = \(\frac{5}{10}\) X \(\frac{4}{5}\) = \(\frac{20}{50}\)
Bs share = \(\frac{3}{10}\) X \(\frac{4}{5}\) = \(\frac{12}{50}\)
Câ€™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 profitsharing 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
Raviâ€™s Share = \(\frac{7}{10}\) – \(\frac{2}{7}\) = \(\frac{29}{70}\)
Mukeshâ€™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 profitsharing ratio.
Solution:
The old ratio of A and B = 7:5
\(\frac{1}{6}\) share of profit is admitted by CA 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 = \(\frac{7}{12}\) – \(\frac{1}{24}\) = \(\frac{13}{24}\)
Bâ€™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 profitsharing ratio of A, B, C and D.
Solution:
The profitsharing ratio of A, B, and C = 3:2:1
Original share of A = \(\frac{3}{6}\)
Dâ€™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 profitsharing 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 \(\frac{1}{2}\) = \(\frac{1}{10}\)
Bharatiâ€™s New Share = \(\frac{3}{5}\) – \(\frac{1}{10}\) = \(\frac{61}{10}\) = \(\frac{5}{10}\)
Asthaâ€™s New share = \(\frac{2}{5}\) – \(\frac{1}{10}\) = \(\frac{41}{10}\) = \(\frac{3}{10}\)
Dinkarâ€™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 profitsharing ratio.
Solution:
The old ratio of X and Y = 3:2
\(\frac{1}{4}\)th share of profit is admitted by ZSacrificing 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
Xâ€™s New Share = \(\frac{3}{5}\) – \(\frac{2}{12}\) = \(\frac{3610}{60}\) = \(\frac{26}{60}\)
Yâ€™s New share = \(\frac{2}{5}\) – \(\frac{1}{2}\) = \(\frac{245}{60}\) = \(\frac{19}{60}\)
Zâ€™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 profitsharing 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
Râ€™s New Share = \(\frac{5}{8}\) – \(\frac{5}{32}\) = \(\frac{15}{32}\)
Sâ€™s New share = \(\frac{3}{8}\) – \(\frac{3}{40}\) = \(\frac{15}{32}\)
Tâ€™s Share = Râ€™s sacrifice + Sâ€™s sacrifice
Tâ€™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 profitsharing 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
Jyotiâ€™s share = \(\frac{2}{10}\) + \(\frac{1}{10}\) = \(\frac{3}{10}\)
New Ratio = Old Ratio – Sacrificing Ratio
Kabirâ€™s New Share = \(\frac{7}{10}\) – \(\frac{2}{10}\) = \(\frac{5}{10}\)
Faridâ€™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 Profitsharing 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
Râ€™s Sacrificing Share = \(\frac{3}{5}\) X \(\frac{1}{4}\) = \(\frac{3}{20}\)
Tâ€™s Sacrificing Share = \(\frac{2}{5}\) X \(\frac{1}{5}\) = \(\frac{2}{25}\)
New Ratio = Old Ratio – Sacrificing Ratio
Râ€™s New Share = \(\frac{3}{5}\) – \(\frac{3}{20}\) = \(\frac{9}{20}\)
Tâ€™s New share = \(\frac{2}{5}\) – \(\frac{2}{25}\) = \(\frac{8}{25}\)
Sâ€™s share = Râ€™s sacrificing share + Tâ€™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 CCombined share of A and B = 1 Câ€˜s share = 1 \(\frac{1}{4}\) = \(\frac{3}{4}\)
New ratio = Combined share of A and B X \(\frac{2}{3}\)
Aâ€™s New Share = \(\frac{3}{4}\) X \(\frac{2}{3}\) = \(\frac{6}{12}\)
Bâ€™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 CAâ€™s sacrifice = Câ€™s share X \(\frac{1}{5}\)
= \(\frac{1}{5}\) X \(\frac{1}{5}\) = \(\frac{1}{25}\)
Bâ€™s sacrifices= Câ€™s share X \(\frac{4}{5}\)
= \(\frac{1}{5}\) X \(\frac{4}{5}\) = \(\frac{4}{25}\)
New Ratio = Old Ratio – Sacrificing Ratio
Aâ€™s share = \(\frac{3}{5}\) – \(\frac{1}{25}\) = \(\frac{151}{25}\)= \(\frac{14}{25}\)
Bâ€™s share = \(\frac{2}{5}\) – \(\frac{4}{25}\) = \(\frac{104}{25}\) = \(\frac{6}{25}\)
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 WAfter admitting W and combining all the partnerâ€™s share , let the share be = 1
X and Y combined share in the new firm = 1 – Zâ€™s share – Wâ€™s share
= 1 – \(\frac{1}{6}\) – \(\frac{1}{6}\) = \(\frac{4}{6}\)
New Ratio = Old Ratio X combined share of X and Y
Xâ€™s share = \(\frac{3}{5}\) X \(\frac{4}{6}\) = \(\frac{12}{30}\)
Yâ€™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 DAfter admitting C and D and combining all the partnerâ€™s share , let the share be = 1
Combined share of profit of A and B after C and Dâ€™s admission = 1 – Câ€™s share – Dâ€™s share
A and B combined share after C and Dâ€™s admission = 1 – Zâ€™s share – Wâ€™s share
= 1 – \(\frac{1}{5}\) – \(\frac{1}{6}\) = \(\frac{19}{30}\)
New Ratio = Old Ratio X combined share of A and B
Aâ€™s share = \(\frac{1}{2}\) X \(\frac{19}{30}\) = \(\frac{19}{60}\)
Bâ€™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 CAfter admitting C and combining all the partnerâ€™s share , let the share be = 1
Combined share of profit of A and B after Dâ€™s admission = 1 – Câ€™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 profitsharing ratio of X, Y, P and Q.
Solution:
The old ratio of X : Y = 3 : 2
Sacrificing ratio = Old ratio X Surrender ratio
Xâ€™s Sacrificing Share = \(\frac{3}{5}\) X \(\frac{1}{3}\) = \(\frac{3}{15}\)
Yâ€™s Sacrificing Share = \(\frac{2}{5}\) X \(\frac{1}{4}\) = \(\frac{2}{20}\)
New Ratio = Old Ratio – Sacrificing Ratio
Xâ€™s share = \(\frac{3}{5}\) – \(\frac{3}{15}\) = \(\frac{6}{15}\)
Yâ€™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
Rakeshâ€™s Share = \(\frac{4}{7}\) – \(\frac{7}{14}\) = \(\frac{1}{14}\)
Sureshâ€™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 profitsharing 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
Aâ€™s Share = \(\frac{3}{5}\) – \(\frac{4}{9}\) = \(\frac{7}{45}\)
Bâ€™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 DLet A, B, C, and D combined share be 1
So, A, B, and C combined share after Dâ€™s admission =1 âˆ’ Dâ€™s share
= 1 \(\frac{1}{3}\) = \(\frac{2}{3}\)
New Ratio = Old Ratio X (combined share of A, B, and C)
Aâ€™s share = \(\frac{4}{9}\) X \(\frac{2}{3}\) = \(\frac{8}{27}\)
Bs share = \(\frac{3}{9}\) X \(\frac{2}{3}\) = \(\frac{6}{27}\)
Câ€™s share = \(\frac{2}{9}\) X \(\frac{2}{3}\) = \(\frac{4}{27}\)
Sacrificing ratio = Old ratio – New ratio
Aâ€™s share = \(\frac{4}{9}\) – \(\frac{8}{27}\) = \(\frac{4}{27}\)
Bâ€™s share = \(\frac{3}{9}\) – \(\frac{6}{27}\) = \(\frac{3}{27}\)
Câ€™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 profitsharing 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 ELet A, B, C, and D combined share be 1
So, A, B, C, and D combined share after Eâ€™s admission =1 âˆ’ Eâ€™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
Aâ€™s share = \(\frac{80}{100}\) X \(\frac{3}{10}\) = \(\frac{24}{100}\)
Bâ€™s share = \(\frac{80}{100}\) X \(\frac{4}{10}\) = \(\frac{32}{100}\)
Câ€™s share = \(\frac{80}{100}\) X \(\frac{2}{10}\) = \(\frac{16}{100}\)
Dâ€™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 profitsharing ratio and sacrificing ratio.
Solution:
Old Ratio = X : Y = 3 : 2
Xâ€™s sacrificing share = \(\frac{1}{3}\) X \(\frac{3}{5}\) = \(\frac{3}{15}\)
Yâ€™s sacrificing share = \(\frac{1}{10}\)
Sacrificing ratio = \(\frac{3}{15}\) : \(\frac{1}{10}\) or 2 : 1
New share = Old Share – Sacrificed Share
Xâ€™s share = \(\frac{3}{5}\) – \(\frac{3}{15}\) = \(\frac{6}{15}\)
Yâ€™s share = \(\frac{2}{5}\) – \(\frac{1}{10}\) = \(\frac{3}{10}\)
Zâ€™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 profitsharing 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 \(\frac{1}{6}\) – \(\frac{1}{5}\) = \(\frac{3056}{30}\) = \(\frac{19}{30}\)
A and B will share the other ratio in 2 : 2 old ratio
Aâ€™s new share = \(\frac{19}{30}\) X \(\frac{2}{4}\) = \(\frac{38}{120}\)
Bâ€™s new share = \(\frac{19}{30}\) X \(\frac{2}{4}\) = \(\frac{28}{120}\)
Câ€™s new share = \(\frac{1}{5}\) X \(\frac{24}{24}\) = \(\frac{24}{120}\)
Dâ€™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
Aâ€™s share = \(\frac{2}{5}\) – \(\frac{19}{60}\) = \(\frac{2419}{60}\) = \(\frac{5}{60}\)
Bâ€™s share = \(\frac{2}{5}\) – \(\frac{19}{60}\) = \(\frac{2419}{60}\) = \(\frac{5}{60}\)
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 profitsharing 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 Eâ€™s admission =1 âˆ’ Eâ€™s share
= 1 \(\frac{1}{4}\) = \(\frac{3}{4}\)
New Ratio = Old ratio X combined share of A and B
Aâ€™s share = \(\frac{3}{5}\) X \(\frac{3}{4}\) = \(\frac{9}{20}\)
Bâ€™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 Câ€™s admission the profit sharing ratio will become old ratio when determining the new profit ratio after Dâ€™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 Dâ€™s admission =1 âˆ’ Dâ€™s share
= 1 \(\frac{20}{100}\) = \(\frac{80}{100}\)
New Ratio = Old ratio X combined share of A, B, and C
Aâ€™s share = \(\frac{9}{20}\) X \(\frac{80}{100}\) = \(\frac{72}{200}\)
Bâ€™s share = \(\frac{6}{20}\) X \(\frac{80}{100}\) = \(\frac{48}{200}\)
Câ€™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 Profitsharing Ratio and Sacrificing Ratio.
Solution:
Old Ratio P : Q = 3 : 2
\(\frac{1}{5}\) of Pâ€™s share is acquired by RRemaining share of P\(\frac{4}{5}\)(1\(\frac{1}{5}\) )of his share from Q
If R share \(\frac{4}{5}\) = \(\frac{1}{25}\)
Pâ€™s share = \(\frac{1}{5}\) X \(\frac{1}{5}\) = \(\frac{1}{25}\)
Qâ€™s share = \(\frac{4}{25}\)
Pâ€™s new share = \(\frac{3}{5}\) – \(\frac{1}{25}\) = \(\frac{151}{25}\) = \(\frac{14}{25}\)
Qâ€™s new share = \(\frac{2}{5}\) – \(\frac{4}{25}\) = \(\frac{104}{25}\) = \(\frac{6}{25}\)
Râ€™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 â‚¹ 15,000. For the purpose of C’s admission, goodwill of the firm is valued at â‚¹ 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 â‚¹ 
Credit â‚¹ 

Aâ€™s Capital A/c 
Dr. 
10,000 

Bâ€™s Capital A/c 
Dr. 
5,000 

To Goodwill A/c 
15,000 

(Goodwill writtenoff 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 Writtenoff Evaluation
Debited Aâ€™s capital = 15,000 X \(\frac{2}{3}\) = â‚¹ 10,000
Credited Bâ€™s capital = 15,000 X \(\frac{1}{3}\) = â‚¹ 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 â‚¹ 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 profitsharing 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 Câ€™s admission = 1 – Câ€™s share
1 \(\frac{1}{4}\) = \(\frac{3}{4}\)
New ratio = Old ratio X combined share of A and B
Aâ€™s share= \(\frac{2}{7}\) X \(\frac{3}{4}\) = \(\frac{6}{28}\)
Bâ€™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
Câ€™s Goodwill share distribution
Câ€™s goodwill share = â‚¹ 14,000
A will receive = 14,000 X \(\frac{2}{7}\) = â‚¹ 4,000
B will receive = 14,000 X \(\frac{5}{7}\) = â‚¹ 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 â‚¹ 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 â‚¹ 
Credit â‚¹ 

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 Aâ€™s Capital A/c 
9,000 

To Bâ€™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
Aâ€™s new ratio share = \(\frac{3}{5}\) – \(\frac{3}{25}\) = \(\frac{12}{25}\)
Bâ€™s new ratio share = \(\frac{2}{5}\) – \(\frac{4}{25}\) = \(\frac{6}{25}\)
Câ€™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 â‚¹ 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 â‚¹ 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 â‚¹ 
Credit â‚¹ 

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 Bâ€™s Capital A/c 
1,200 

To Câ€™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 â‚¹ 
Credit â‚¹ 

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 Bâ€™s Capital A/c 
1,400 

To Câ€™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 â‚¹ 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 â‚¹ 
Credit â‚¹ 

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 Bâ€™s Capital A/c 
15,000 

(Goodwill premium transferred to Bâ€™s Capital) 

Câ€™s Capital A/c 
Dr. 
3,750 

To Bâ€™s Capital A/c 
3,750 

(Being charges goodwill from Câ€™s capital A/c due to his gain in profit sharing) 
Working Notes 1: Sacrificing Ratio Evaluation
Let B and C combined share after Dâ€™s be 1
B and C combined share after Dâ€™s admission = 1 – Dâ€™s share
1 \(\frac{1}{3}\) = \(\frac{2}{3}\)
Profit sharing of B and C after Dâ€™s admission = \(\frac{2}{3}\) X \(\frac{1}{2}\) = \(\frac{1}{3}\) each
Sacrificing ratio = New ratio – New ratio
Bâ€™s share = \(\frac{3}{4}\) – \(\frac{1}{3}\) = \(\frac{5}{12}\) (sacrificing)
Câ€™s share = \(\frac{1}{4}\) – \(\frac{1}{3}\) = \(\frac{1}{12}\) (gain)
Working Notes 2:
C gains in the new firm. So, Câ€™s goodwill gain will be debited from his capital A/c and given to the sacrificing partner B.
Firmâ€™s goodwill = Goodwill premium brought by D X Reciprocal of Dâ€™s share
= 15,000 X \(\frac{3}{1}\) = â‚¹ 45,000
Câ€™s share of Goodwill gain = Firm goodwill X Share of gain
= 45,000 X \(\frac{1}{12}\) = â‚¹ 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 profitsharing ratio between M, J and R will be 5 : 3 : 2. R brought in â‚¹ 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 â‚¹ 
Credit â‚¹ 

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 Mâ€™s Capital A/c 
12,500 

To Jâ€™s Capital A/c 
12,500 

(Distributed Câ€™s Goodwill share between M and J in their sacrificing ratio) 
Working Notes 1: Sacrificing Ratio Evaluation
Sacrificing ratio = Old ratio – New ratio
Mâ€™s sacrificing ratio = \(\frac{3}{5}\) – \(\frac{5}{10}\) = \(\frac{1}{10}\)
Jâ€™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: Râ€™s goodwill share Evaluation
Mâ€™s goodwill share = 25,000 X \(\frac{1}{2}\) = â‚¹ 12,500
Jâ€™s goodwill share = 25,000 X \(\frac{1}{2}\) = â‚¹ 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 â‚¹ 40,000 as capital and the necessary amount of goodwill which is valued at â‚¹ 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 profitsharing ratio of the partners.
Solution:
Journal 

Date 
Particulars 
L.F. 
Debit â‚¹ 
Credit â‚¹ 

Cash A/c 
Dr. 
52,000 

To Câ€™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 Aâ€™s Capital A/c 
6,000 

To Bâ€™s Capital A/c 
6,000 

(Being Câ€™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
Aâ€™s share = \(\frac{5}{8}\) – \(\frac{1}{10}\) = \(\frac{21}{40}\)
Bâ€™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 Râ€™s goodwill share Evaluation
Aâ€™s goodwill share = 12,000 X \(\frac{1}{2}\) = â‚¹ 6,000
Bâ€™s goodwill share = 12,000 X \(\frac{1}{2}\) = â‚¹ 6,000
So, A and B will receive 6,000 each
Also Check:Â Important Questions forÂ Admission of a partner
The aboveprovided solutions are considered to be the best solutions for â€˜TS Grewal Solutions Class 12 Accountancy Vol 1 Chapter 5 Admission of a partnerâ€™. Stay tuned to BYJUâ€™S to learn more and score well in the upcoming board examinations.
Important Topics in Accountancy: 