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.
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-
\(\begin{array}{l}\frac{1}{5}\end{array} \)
=
\(\begin{array}{l}\frac{4}{5}\end{array} \)
(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 =
\(\begin{array}{l}\frac{5}{10}\end{array} \)
X
\(\begin{array}{l}\frac{4}{5}\end{array} \)
=
\(\begin{array}{l}\frac{20}{50}\end{array} \)
Ys share =
\(\begin{array}{l}\frac{3}{10}\end{array} \)
X
\(\begin{array}{l}\frac{4}{5}\end{array} \)
=
\(\begin{array}{l}\frac{12}{50}\end{array} \)
Z’s share =
\(\begin{array}{l}\frac{2}{10}\end{array} \)
X
\(\begin{array}{l}\frac{4}{5}\end{array} \)
=
\(\begin{array}{l}\frac{8}{50}\end{array} \)
So, the profit sharing ratio between X, Y, Z, and A will be
\(\begin{array}{l}\frac{20}{50}\end{array} \)
:
\(\begin{array}{l}\frac{12}{50}\end{array} \)
:
\(\begin{array}{l}\frac{8}{50}\end{array} \)
:
\(\begin{array}{l}\frac{1}{50}\end{array} \)
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
\(\begin{array}{l}\frac{7}{10}\end{array} \)
:
\(\begin{array}{l}\frac{3}{10}\end{array} \)
\(\begin{array}{l}\frac{3}{7}\end{array} \)
share of profit is admitted by Ashok
Ravi sacrifice
\(\begin{array}{l}\frac{2}{7}\end{array} \)
in favour of Ashok
Mukesh sacrifice
\(\begin{array}{l}\frac{1}{7}\end{array} \)
in favour of Ashok
New Ratio = Old Ratio – Sacrificing Ratio
Ravi’s Share =
\(\begin{array}{l}\frac{7}{10}\end{array} \)
–
\(\begin{array}{l}\frac{2}{7}\end{array} \)
=
\(\begin{array}{l}\frac{29}{70}\end{array} \)
Mukesh’s share =
\(\begin{array}{l}\frac{3}{10}\end{array} \)
–
\(\begin{array}{l}\frac{1}{7}\end{array} \)
=
\(\begin{array}{l}\frac{11}{70}\end{array} \)
So, the new profit sharing ratio between Ravi, Mukesh, and Ashok will be,
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
\(\begin{array}{l}\frac{1}{6}\end{array} \)
share of profit is admitted by C
A sacrifice
\(\begin{array}{l}\frac{1}{24}\end{array} \)
in favour of C
B sacrifice
\(\begin{array}{l}\frac{1}{8}\end{array} \)
in favour of C
New Ratio = Old Ratio – Sacrificing Ratio
As Share =
\(\begin{array}{l}\frac{7}{12}\end{array} \)
–
\(\begin{array}{l}\frac{1}{24}\end{array} \)
=
\(\begin{array}{l}\frac{13}{24}\end{array} \)
B’s share =
\(\begin{array}{l}\frac{5}{12}\end{array} \)
–
\(\begin{array}{l}\frac{1}{8}\end{array} \)
=
\(\begin{array}{l}\frac{7}{24}\end{array} \)
So, the new profit sharing ratio between A, B, and C will be =
\(\begin{array}{l}\frac{13}{24}\end{array} \)
:
\(\begin{array}{l}\frac{7}{24}\end{array} \)
:
\(\begin{array}{l}\frac{1}{6}\end{array} \)
=
\(\begin{array}{l}\frac{13:7:4}{24}\end{array} \)
= 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 =
\(\begin{array}{l}\frac{3}{6}\end{array} \)
D’s share =
\(\begin{array}{l}\frac{1}{8}\end{array} \)
(out of which
\(\begin{array}{l}\frac{1}{6}\end{array} \)
is acquired from B and C each
New share of B =
\(\begin{array}{l}\frac{2}{6}\end{array} \)
–
\(\begin{array}{l}\frac{1}{16}\end{array} \)
=
\(\begin{array}{l}\frac{13}{48}\end{array} \)
New share of C =
\(\begin{array}{l}\frac{1}{6}\end{array} \)
–
\(\begin{array}{l}\frac{1}{16}\end{array} \)
=
\(\begin{array}{l}\frac{5}{48}\end{array} \)
So, the new profit sharing ratio between A, B, C, and D is =
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 =
\(\begin{array}{l}\frac{1}{5}\end{array} \)
Bharati sacrifices =
\(\begin{array}{l}\frac{1}{5}\end{array} \)
X
\(\begin{array}{l}\frac{1}{2}\end{array} \)
=
\(\begin{array}{l}\frac{1}{10}\end{array} \)
Astha sacrifices =
\(\begin{array}{l}\frac{1}{5}\end{array} \)
X
\(\begin{array}{l}\frac{1}{2}\end{array} \)
=
\(\begin{array}{l}\frac{1}{10}\end{array} \)
Bharati’s New Share =
\(\begin{array}{l}\frac{3}{5}\end{array} \)
–
\(\begin{array}{l}\frac{1}{10}\end{array} \)
=
\(\begin{array}{l}\frac{6-1}{10}\end{array} \)
=
\(\begin{array}{l}\frac{5}{10}\end{array} \)
Astha’s New share =
\(\begin{array}{l}\frac{2}{5}\end{array} \)
–
\(\begin{array}{l}\frac{1}{10}\end{array} \)
=
\(\begin{array}{l}\frac{4-1}{10}\end{array} \)
=
\(\begin{array}{l}\frac{3}{10}\end{array} \)
Dinkar’s New share =
\(\begin{array}{l}\frac{1}{5}\end{array} \)
X
\(\begin{array}{l}\frac{2}{2}\end{array} \)
=
\(\begin{array}{l}\frac{2}{10}\end{array} \)
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
\(\begin{array}{l}\frac{1}{4}\end{array} \)
th share of profit is admitted by Z
Sacrificing ratio of X and Y is 2:1
Z acquired share from X =
\(\begin{array}{l}\frac{2}{3}\end{array} \)
X
\(\begin{array}{l}\frac{1}{4}\end{array} \)
=
\(\begin{array}{l}\frac{2}{12}\end{array} \)
Z acquired share from Y =
\(\begin{array}{l}\frac{1}{3}\end{array} \)
X
\(\begin{array}{l}\frac{1}{4}\end{array} \)
=
\(\begin{array}{l}\frac{2}{12}\end{array} \)
New Ratio = Old ratio – Sacrificing ratio
X’s New Share =
\(\begin{array}{l}\frac{3}{5}\end{array} \)
–
\(\begin{array}{l}\frac{2}{12}\end{array} \)
=
\(\begin{array}{l}\frac{36-10}{60}\end{array} \)
=
\(\begin{array}{l}\frac{26}{60}\end{array} \)
Y’s New share =
\(\begin{array}{l}\frac{2}{5}\end{array} \)
–
\(\begin{array}{l}\frac{1}{2}\end{array} \)
=
\(\begin{array}{l}\frac{24-5}{60}\end{array} \)
=
\(\begin{array}{l}\frac{19}{60}\end{array} \)
Z’s New share =
\(\begin{array}{l}\frac{1}{4}\end{array} \)
X
\(\begin{array}{l}\frac{15}{15}\end{array} \)
=
\(\begin{array}{l}\frac{15}{60}\end{array} \)
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.
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
\(\begin{array}{l}\frac{2}{10}\end{array} \)
in favour of Jyoti
Farid sacrifice
\(\begin{array}{l}\frac{1}{10}\end{array} \)
in favour of Jyoti
Jyoti’s share =
\(\begin{array}{l}\frac{2}{10}\end{array} \)
+
\(\begin{array}{l}\frac{1}{10}\end{array} \)
=
\(\begin{array}{l}\frac{3}{10}\end{array} \)
New Ratio = Old Ratio – Sacrificing Ratio
Kabir’s New Share =
\(\begin{array}{l}\frac{7}{10}\end{array} \)
–
\(\begin{array}{l}\frac{2}{10}\end{array} \)
=
\(\begin{array}{l}\frac{5}{10}\end{array} \)
Farid’s New share =
\(\begin{array}{l}\frac{3}{10}\end{array} \)
–
\(\begin{array}{l}\frac{1}{10}\end{array} \)
=
\(\begin{array}{l}\frac{2}{10}\end{array} \)
So, the new profit sharing ratio between Kabir, Farid, and Jyoti will be = 5 : 2 : 3
The Sacrificing ratio of Kabir and Farid is
\(\begin{array}{l}\frac{2}{10}\end{array} \)
and
\(\begin{array}{l}\frac{1}{10}\end{array} \)
= 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.
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 =
\(\begin{array}{l}\frac{3}{5}\end{array} \)
X
\(\begin{array}{l}\frac{1}{3}\end{array} \)
=
\(\begin{array}{l}\frac{3}{15}\end{array} \)
Y’s Sacrificing Share =
\(\begin{array}{l}\frac{2}{5}\end{array} \)
X
\(\begin{array}{l}\frac{1}{4}\end{array} \)
=
\(\begin{array}{l}\frac{2}{20}\end{array} \)
New Ratio = Old Ratio – Sacrificing Ratio
X’s share =
\(\begin{array}{l}\frac{3}{5}\end{array} \)
–
\(\begin{array}{l}\frac{3}{15}\end{array} \)
=
\(\begin{array}{l}\frac{6}{15}\end{array} \)
Y’s share =
\(\begin{array}{l}\frac{2}{5}\end{array} \)
–
\(\begin{array}{l}\frac{2}{20}\end{array} \)
=
\(\begin{array}{l}\frac{6}{20}\end{array} \)
X sacrificed for P =
\(\begin{array}{l}\frac{3}{15}\end{array} \)
Y sacrificed for Q =
\(\begin{array}{l}\frac{2}{10}\end{array} \)
So, the profit sharing ratio between X, Y, P, and Q will be
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 =
\(\begin{array}{l}\frac{4}{7}\end{array} \)
–
\(\begin{array}{l}\frac{7}{14}\end{array} \)
=
\(\begin{array}{l}\frac{1}{14}\end{array} \)
Suresh’s Share =
\(\begin{array}{l}\frac{3}{7}\end{array} \)
–
\(\begin{array}{l}\frac{4}{14}\end{array} \)
=
\(\begin{array}{l}\frac{2}{14}\end{array} \)
So, sacrificing ratio of Rakesh and Suresh =
\(\begin{array}{l}\frac{1}{14}\end{array} \)
:
\(\begin{array}{l}\frac{2}{14}\end{array} \)
= 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 =
\(\begin{array}{l}\frac{3}{5}\end{array} \)
–
\(\begin{array}{l}\frac{4}{9}\end{array} \)
=
\(\begin{array}{l}\frac{7}{45}\end{array} \)
B’s Share =
\(\begin{array}{l}\frac{2}{5}\end{array} \)
–
\(\begin{array}{l}\frac{3}{9}\end{array} \)
=
\(\begin{array}{l}\frac{3}{45}\end{array} \)
So, sacrificing ratio of A and B =
\(\begin{array}{l}\frac{7}{45}\end{array} \)
:
\(\begin{array}{l}\frac{3}{45}\end{array} \)
= 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
\(\begin{array}{l}\frac{1}{3}\end{array} \)
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-
\(\begin{array}{l}\frac{1}{3}\end{array} \)
=
\(\begin{array}{l}\frac{2}{3}\end{array} \)
New Ratio = Old Ratio X (combined share of A, B, and C)
A’s share =
\(\begin{array}{l}\frac{4}{9}\end{array} \)
X
\(\begin{array}{l}\frac{2}{3}\end{array} \)
=
\(\begin{array}{l}\frac{8}{27}\end{array} \)
Bs share =
\(\begin{array}{l}\frac{3}{9}\end{array} \)
X
\(\begin{array}{l}\frac{2}{3}\end{array} \)
=
\(\begin{array}{l}\frac{6}{27}\end{array} \)
C’s share =
\(\begin{array}{l}\frac{2}{9}\end{array} \)
X
\(\begin{array}{l}\frac{2}{3}\end{array} \)
=
\(\begin{array}{l}\frac{4}{27}\end{array} \)
Sacrificing ratio = Old ratio – New ratio
A’s share =
\(\begin{array}{l}\frac{4}{9}\end{array} \)
–
\(\begin{array}{l}\frac{8}{27}\end{array} \)
=
\(\begin{array}{l}\frac{4}{27}\end{array} \)
B’s share =
\(\begin{array}{l}\frac{3}{9}\end{array} \)
–
\(\begin{array}{l}\frac{6}{27}\end{array} \)
=
\(\begin{array}{l}\frac{3}{27}\end{array} \)
C’s share =
\(\begin{array}{l}\frac{2}{7}\end{array} \)
–
\(\begin{array}{l}\frac{4}{27}\end{array} \)
=
\(\begin{array}{l}\frac{2}{27}\end{array} \)
So, sacrificing ratio of A : B : C will be
\(\begin{array}{l}\frac{4}{27}\end{array} \)
:
\(\begin{array}{l}\frac{3}{27}\end{array} \)
:
\(\begin{array}{l}\frac{2}{27}\end{array} \)
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
\(\begin{array}{l}\frac{20}{100}\end{array} \)
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-
\(\begin{array}{l}\frac{20}{100}\end{array} \)
=
\(\begin{array}{l}\frac{80}{100}\end{array} \)
New Ratio = Combined share of A, B, C, and D X Agreed share of A, B, C, and D
A’s share =
\(\begin{array}{l}\frac{80}{100}\end{array} \)
X
\(\begin{array}{l}\frac{3}{10}\end{array} \)
=
\(\begin{array}{l}\frac{24}{100}\end{array} \)
B’s share =
\(\begin{array}{l}\frac{80}{100}\end{array} \)
X
\(\begin{array}{l}\frac{4}{10}\end{array} \)
=
\(\begin{array}{l}\frac{32}{100}\end{array} \)
C’s share =
\(\begin{array}{l}\frac{80}{100}\end{array} \)
X
\(\begin{array}{l}\frac{2}{10}\end{array} \)
=
\(\begin{array}{l}\frac{16}{100}\end{array} \)
D’s share =
\(\begin{array}{l}\frac{80}{100}\end{array} \)
X
\(\begin{array}{l}\frac{1}{10}\end{array} \)
=
\(\begin{array}{l}\frac{8}{100}\end{array} \)
New sacrificing ratio of A : B : C : D : E =
\(\begin{array}{l}\frac{24}{100}\end{array} \)
:
\(\begin{array}{l}\frac{32}{100}\end{array} \)
:
\(\begin{array}{l}\frac{16}{100}\end{array} \)
:
\(\begin{array}{l}\frac{8}{100}\end{array} \)
:
\(\begin{array}{l}\frac{20}{100}\end{array} \)
= 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 =
\(\begin{array}{l}\frac{1}{3}\end{array} \)
X
\(\begin{array}{l}\frac{3}{5}\end{array} \)
=
\(\begin{array}{l}\frac{3}{15}\end{array} \)
Y’s sacrificing share =
\(\begin{array}{l}\frac{1}{10}\end{array} \)
Sacrificing ratio =
\(\begin{array}{l}\frac{3}{15}\end{array} \)
:
\(\begin{array}{l}\frac{1}{10}\end{array} \)
or 2 : 1
New share = Old Share – Sacrificed Share
X’s share =
\(\begin{array}{l}\frac{3}{5}\end{array} \)
–
\(\begin{array}{l}\frac{3}{15}\end{array} \)
=
\(\begin{array}{l}\frac{6}{15}\end{array} \)
Y’s share =
\(\begin{array}{l}\frac{2}{5}\end{array} \)
–
\(\begin{array}{l}\frac{1}{10}\end{array} \)
=
\(\begin{array}{l}\frac{3}{10}\end{array} \)
Z’s share =
\(\begin{array}{l}\frac{3}{15}\end{array} \)
–
\(\begin{array}{l}\frac{1}{10}\end{array} \)
=
\(\begin{array}{l}\frac{9}{30}\end{array} \)
New Ratio =
\(\begin{array}{l}\frac{6}{15}\end{array} \)
:
\(\begin{array}{l}\frac{3}{10}\end{array} \)
:
\(\begin{array}{l}\frac{9}{30}\end{array} \)
= 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
\(\begin{array}{l}\frac{1}{6}\end{array} \)
th share and C retained his share
\(\begin{array}{l}\frac{1}{5}\end{array} \)
Remaining Share = 1-
\(\begin{array}{l}\frac{1}{6}\end{array} \)
–
\(\begin{array}{l}\frac{1}{5}\end{array} \)
=
\(\begin{array}{l}\frac{30-5-6}{30}\end{array} \)
=
\(\begin{array}{l}\frac{19}{30}\end{array} \)
A and B will share the other ratio in 2 : 2 old ratio
A’s new share =
\(\begin{array}{l}\frac{19}{30}\end{array} \)
X
\(\begin{array}{l}\frac{2}{4}\end{array} \)
=
\(\begin{array}{l}\frac{38}{120}\end{array} \)
B’s new share =
\(\begin{array}{l}\frac{19}{30}\end{array} \)
X
\(\begin{array}{l}\frac{2}{4}\end{array} \)
=
\(\begin{array}{l}\frac{28}{120}\end{array} \)
C’s new share =
\(\begin{array}{l}\frac{1}{5}\end{array} \)
X
\(\begin{array}{l}\frac{24}{24}\end{array} \)
=
\(\begin{array}{l}\frac{24}{120}\end{array} \)
D’s new share =
\(\begin{array}{l}\frac{1}{6}\end{array} \)
X
\(\begin{array}{l}\frac{20}{20}\end{array} \)
=
\(\begin{array}{l}\frac{20}{120}\end{array} \)
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 =
\(\begin{array}{l}\frac{2}{5}\end{array} \)
–
\(\begin{array}{l}\frac{19}{60}\end{array} \)
=
\(\begin{array}{l}\frac{24-19}{60}\end{array} \)
=
\(\begin{array}{l}\frac{5}{60}\end{array} \)
B’s share =
\(\begin{array}{l}\frac{2}{5}\end{array} \)
–
\(\begin{array}{l}\frac{19}{60}\end{array} \)
=
\(\begin{array}{l}\frac{24-19}{60}\end{array} \)
=
\(\begin{array}{l}\frac{5}{60}\end{array} \)
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
\(\begin{array}{l}\frac{1}{6}\end{array} \)
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-
\(\begin{array}{l}\frac{1}{4}\end{array} \)
=
\(\begin{array}{l}\frac{3}{4}\end{array} \)
New Ratio = Old ratio X combined share of A and B
A’s share =
\(\begin{array}{l}\frac{3}{5}\end{array} \)
X
\(\begin{array}{l}\frac{3}{4}\end{array} \)
=
\(\begin{array}{l}\frac{9}{20}\end{array} \)
B’s share =
\(\begin{array}{l}\frac{2}{5}\end{array} \)
X
\(\begin{array}{l}\frac{3}{4}\end{array} \)
=
\(\begin{array}{l}\frac{6}{20}\end{array} \)
New profit sharing ratio after admission of C = A : B : C =
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
\(\begin{array}{l}\frac{20}{100}\end{array} \)
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-
\(\begin{array}{l}\frac{20}{100}\end{array} \)
=
\(\begin{array}{l}\frac{80}{100}\end{array} \)
New Ratio = Old ratio X combined share of A, B, and C
A’s share =
\(\begin{array}{l}\frac{9}{20}\end{array} \)
X
\(\begin{array}{l}\frac{80}{100}\end{array} \)
=
\(\begin{array}{l}\frac{72}{200}\end{array} \)
B’s share =
\(\begin{array}{l}\frac{6}{20}\end{array} \)
X
\(\begin{array}{l}\frac{80}{100}\end{array} \)
=
\(\begin{array}{l}\frac{48}{200}\end{array} \)
C’s share =
\(\begin{array}{l}\frac{5}{20}\end{array} \)
X
\(\begin{array}{l}\frac{80}{100}\end{array} \)
=
\(\begin{array}{l}\frac{40}{200}\end{array} \)
So, new profit sharing ratio between A : B : C : D will be
\(\begin{array}{l}\frac{72}{200}\end{array} \)
:
\(\begin{array}{l}\frac{48}{200}\end{array} \)
:
\(\begin{array}{l}\frac{40}{200}\end{array} \)
:
\(\begin{array}{l}\frac{20}{100}\end{array} \)
= 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
\(\begin{array}{l}\frac{1}{5}\end{array} \)
of P’s share is acquired by R
Remaining share of P
\(\begin{array}{l}\frac{4}{5}\end{array} \)
(1-
\(\begin{array}{l}\frac{1}{5}\end{array} \)
)of his share from Q
If R share
\(\begin{array}{l}\frac{4}{5}\end{array} \)
=
\(\begin{array}{l}\frac{1}{25}\end{array} \)
P’s share =
\(\begin{array}{l}\frac{1}{5}\end{array} \)
X
\(\begin{array}{l}\frac{1}{5}\end{array} \)
=
\(\begin{array}{l}\frac{1}{25}\end{array} \)
Q’s share =
\(\begin{array}{l}\frac{4}{25}\end{array} \)
P’s new share =
\(\begin{array}{l}\frac{3}{5}\end{array} \)
–
\(\begin{array}{l}\frac{1}{25}\end{array} \)
=
\(\begin{array}{l}\frac{15-1}{25}\end{array} \)
=
\(\begin{array}{l}\frac{14}{25}\end{array} \)
Q’s new share =
\(\begin{array}{l}\frac{2}{5}\end{array} \)
–
\(\begin{array}{l}\frac{4}{25}\end{array} \)
=
\(\begin{array}{l}\frac{10-4}{25}\end{array} \)
=
\(\begin{array}{l}\frac{6}{25}\end{array} \)
R’s new share =
\(\begin{array}{l}\frac{1}{5}\end{array} \)
X
\(\begin{array}{l}\frac{5}{5}\end{array} \)
=
\(\begin{array}{l}\frac{5}{25}\end{array} \)
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
\(\begin{array}{l}\frac{2}{3}\end{array} \)
= ₹ 10,000
Credited B’s capital = 15,000 X
\(\begin{array}{l}\frac{1}{3}\end{array} \)
= ₹ 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
\(\begin{array}{l}\frac{1}{4}\end{array} \)
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
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 =
\(\begin{array}{l}\frac{3}{5}\end{array} \)
X
\(\begin{array}{l}\frac{1}{5}\end{array} \)
=
\(\begin{array}{l}\frac{3}{25}\end{array} \)
B sacrifices =
\(\begin{array}{l}\frac{2}{5}\end{array} \)
X
\(\begin{array}{l}\frac{2}{5}\end{array} \)
=
\(\begin{array}{l}\frac{4}{25}\end{array} \)
Sacrificing ratio of A : B =
\(\begin{array}{l}\frac{3}{25}\end{array} \)
:
\(\begin{array}{l}\frac{4}{25}\end{array} \)
= 3 : 4
New ratio – Old ratio – Sacrificing ratio
A’s new ratio share =
\(\begin{array}{l}\frac{3}{5}\end{array} \)
–
\(\begin{array}{l}\frac{3}{25}\end{array} \)
=
\(\begin{array}{l}\frac{12}{25}\end{array} \)
B’s new ratio share =
\(\begin{array}{l}\frac{2}{5}\end{array} \)
–
\(\begin{array}{l}\frac{4}{25}\end{array} \)
=
\(\begin{array}{l}\frac{6}{25}\end{array} \)
C’s new ratio share = A sacrifice + B sacrifice =
\(\begin{array}{l}\frac{3}{25}\end{array} \)
+
\(\begin{array}{l}\frac{4}{25}\end{array} \)
=
\(\begin{array}{l}\frac{7}{25}\end{array} \)
So, New ratio A : B : C = 12 : 6 : 7
Goodwill premium bought by C= 75,000 X
\(\begin{array}{l}\frac{7}{25}\end{array} \)
= 21, 000
Goodwill premium distribution
Goodwill of A = 21,000 X
\(\begin{array}{l}\frac{3}{7}\end{array} \)
= 9, 000
Goodwill of B = 21,000 X
\(\begin{array}{l}\frac{4}{7}\end{array} \)
= 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
\(\begin{array}{l}\frac{3}{5}\end{array} \)
= 1,200
Goodwill of C = 2,000 X
\(\begin{array}{l}\frac{2}{5}\end{array} \)
= 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}\end{array} \)
: latex]\frac{1}{12}\end{array} \)
= 2 : 1
Working Note 2 : Distribution of goodwill premium
Goodwill of B = 2,100 X
\(\begin{array}{l}\frac{2}{3}\end{array} \)
= 1,400
Goodwill of C = 2,100 X
\(\begin{array}{l}\frac{1}{5}\end{array} \)
= 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-
\(\begin{array}{l}\frac{1}{3}\end{array} \)
=
\(\begin{array}{l}\frac{2}{3}\end{array} \)
Profit sharing of B and C after D’s admission =
\(\begin{array}{l}\frac{2}{3}\end{array} \)
X
\(\begin{array}{l}\frac{1}{2}\end{array} \)
=
\(\begin{array}{l}\frac{1}{3}\end{array} \)
each
Sacrificing ratio = New ratio – New ratio
B’s share =
\(\begin{array}{l}\frac{3}{4}\end{array} \)
–
\(\begin{array}{l}\frac{1}{3}\end{array} \)
=
\(\begin{array}{l}\frac{5}{12}\end{array} \)
(sacrificing)
C’s share =
\(\begin{array}{l}\frac{1}{4}\end{array} \)
–
\(\begin{array}{l}\frac{1}{3}\end{array} \)
=
\(\begin{array}{l}\frac{-1}{12}\end{array} \)
(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
\(\begin{array}{l}\frac{3}{1}\end{array} \)
= ₹ 45,000
C’s share of Goodwill gain = Firm goodwill X Share of gain
= 45,000 X
\(\begin{array}{l}\frac{1}{12}\end{array} \)
= ₹ 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 =
\(\begin{array}{l}\frac{3}{5}\end{array} \)
–
\(\begin{array}{l}\frac{5}{10}\end{array} \)
=
\(\begin{array}{l}\frac{1}{10}\end{array} \)
J’s sacrificing ratio =
\(\begin{array}{l}\frac{2}{5}\end{array} \)
–
\(\begin{array}{l}\frac{3}{10}\end{array} \)
=
\(\begin{array}{l}\frac{1}{10}\end{array} \)
Sacrificing ratio = M : J =
\(\begin{array}{l}\frac{1}{10}\end{array} \)
:
\(\begin{array}{l}\frac{1}{10}\end{array} \)
= 1 : 1
Working Notes 2: R’s goodwill share Evaluation
M’s goodwill share = 25,000 X
\(\begin{array}{l}\frac{1}{2}\end{array} \)
= ₹ 12,500
J’s goodwill share = 25,000 X
\(\begin{array}{l}\frac{1}{2}\end{array} \)
= ₹ 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 =
\(\begin{array}{l}\frac{1}{10}\end{array} \)
:
\(\begin{array}{l}\frac{1}{10}\end{array} \)
= 1 : 1
Working Notes 1 : A and B Sacrificing Ratio
Working Notes 2 : New Profit Sharing Ratio Evaluation
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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