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

TS Grewal Solutions Class 12 Accountancy Vol 1 Chapter 5

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

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

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

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

Ravi

\(\begin{array}{l}\frac{29}{70}\end{array} \)
: Mukesh
\(\begin{array}{l}\frac{11}{70}\end{array} \)
: Ashok
\(\begin{array}{l}\frac{3}{7}\end{array} \)
=
\(\begin{array}{l}\frac{29:11:3}{70}\end{array} \)
= 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

\(\begin{array}{l}\frac{1}{6}\end{array} \)
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 =

\(\begin{array}{l}\frac{3}{6}\end{array} \)
:
\(\begin{array}{l}\frac{13}{48}\end{array} \)
:
\(\begin{array}{l}\frac{5}{48}\end{array} \)
:
\(\begin{array}{l}\frac{1}{8}\end{array} \)
=
\(\begin{array}{l}\frac{24:13:5:6}{48}\end{array} \)
= 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 =

\(\begin{array}{l}\frac{1}{5}\end{array} \)

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.

Solution:

The old ratio of R and S = 5 : 3

Sacrificing ratio = Old Ratio X Surrender Ratio

Sacrificing ratio of R and =

\(\begin{array}{l}\frac{5}{8}\end{array} \)
X
\(\begin{array}{l}\frac{1}{4}\end{array} \)
=
\(\begin{array}{l}\frac{5}{32}\end{array} \)

Sacrificing ratio of S and =

\(\begin{array}{l}\frac{3}{8}\end{array} \)
X
\(\begin{array}{l}\frac{1}{5}\end{array} \)
=
\(\begin{array}{l}\frac{3}{40}\end{array} \)

New Ratio = Old Ratio – Sacrificing Ratio

R’s New Share =

\(\begin{array}{l}\frac{5}{8}\end{array} \)
\(\begin{array}{l}\frac{5}{32}\end{array} \)
=
\(\begin{array}{l}\frac{15}{32}\end{array} \)

S’s New share =

\(\begin{array}{l}\frac{3}{8}\end{array} \)
\(\begin{array}{l}\frac{3}{40}\end{array} \)
=
\(\begin{array}{l}\frac{15}{32}\end{array} \)

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

T’s Share =

\(\begin{array}{l}\frac{5}{32}\end{array} \)
+
\(\begin{array}{l}\frac{3}{40}\end{array} \)
=
\(\begin{array}{l}\frac{25+12}{160}\end{array} \)
=
\(\begin{array}{l}\frac{37}{160}\end{array} \)

New profit sharing ratio between R, S, and T =

\(\begin{array}{l}\frac{15}{32}\end{array} \)
:
\(\begin{array}{l}\frac{15}{32}\end{array} \)
:
\(\begin{array}{l}\frac{37}{160}\end{array} \)
=
\(\begin{array}{l}\frac{75:48:37}{160}\end{array} \)
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

\(\begin{array}{l}\frac{2}{10}\end{array} \)
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.

Solution:

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

Sacrificing ratio = Old ratio X Surrender ratio

R’s Sacrificing Share =

\(\begin{array}{l}\frac{3}{5}\end{array} \)
X
\(\begin{array}{l}\frac{1}{4}\end{array} \)
=
\(\begin{array}{l}\frac{3}{20}\end{array} \)

T’s Sacrificing Share =

\(\begin{array}{l}\frac{2}{5}\end{array} \)
X
\(\begin{array}{l}\frac{1}{5}\end{array} \)
=
\(\begin{array}{l}\frac{2}{25}\end{array} \)

New Ratio = Old Ratio – Sacrificing Ratio

R’s New Share =

\(\begin{array}{l}\frac{3}{5}\end{array} \)
\(\begin{array}{l}\frac{3}{20}\end{array} \)
=
\(\begin{array}{l}\frac{9}{20}\end{array} \)

T’s New share =

\(\begin{array}{l}\frac{2}{5}\end{array} \)
\(\begin{array}{l}\frac{2}{25}\end{array} \)
=
\(\begin{array}{l}\frac{8}{25}\end{array} \)

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

=

\(\begin{array}{l}\frac{3}{20}\end{array} \)
+
\(\begin{array}{l}\frac{2}{25}\end{array} \)
=
\(\begin{array}{l}\frac{23}{100}\end{array} \)

So, the new profit sharing ratio between R, T, and S will be =

\(\begin{array}{l}\frac{9}{20}\end{array} \)
:
\(\begin{array}{l}\frac{8}{25}\end{array} \)
:
\(\begin{array}{l}\frac{23}{100}\end{array} \)
=
\(\begin{array}{l}\frac{45: 32 : 23}{100}\end{array} \)
or 45: 32 : 23

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

\(\begin{array}{l}\frac{1}{4}\end{array} \)
th profit share is admitted by C

Combined share of A and B = 1- C‘s share = 1-

\(\begin{array}{l}\frac{1}{4}\end{array} \)
=
\(\begin{array}{l}\frac{3}{4}\end{array} \)

New ratio = Combined share of A and B X

\(\begin{array}{l}\frac{2}{3}\end{array} \)

A’s New Share =

\(\begin{array}{l}\frac{3}{4}\end{array} \)
X
\(\begin{array}{l}\frac{2}{3}\end{array} \)
=
\(\begin{array}{l}\frac{6}{12}\end{array} \)

B’s New share =

\(\begin{array}{l}\frac{3}{4}\end{array} \)
X
\(\begin{array}{l}\frac{1}{3}\end{array} \)
=
\(\begin{array}{l}\frac{3}{12}\end{array} \)

New Profit sharing ratio A : B : C =

\(\begin{array}{l}\frac{6}{12}\end{array} \)
:
\(\begin{array}{l}\frac{3}{12}\end{array} \)
:
\(\begin{array}{l}\frac{1}{4}\end{array} \)
=
\(\begin{array}{l}\frac{6: 3 : 3}{100}\end{array} \)
= 2 : 1 :1

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

\(\begin{array}{l}\frac{1}{5}\end{array} \)
th profit share is admitted by C

A’s sacrifice = C’s share X

\(\begin{array}{l}\frac{1}{5}\end{array} \)

=

\(\begin{array}{l}\frac{1}{5}\end{array} \)
X
\(\begin{array}{l}\frac{1}{5}\end{array} \)
=
\(\begin{array}{l}\frac{1}{25}\end{array} \)

B’s sacrifices= C’s share X

\(\begin{array}{l}\frac{4}{5}\end{array} \)

=

\(\begin{array}{l}\frac{1}{5}\end{array} \)
X
\(\begin{array}{l}\frac{4}{5}\end{array} \)
=
\(\begin{array}{l}\frac{4}{25}\end{array} \)

New Ratio = Old Ratio – Sacrificing Ratio

A’s share =

\(\begin{array}{l}\frac{3}{5}\end{array} \)
\(\begin{array}{l}\frac{1}{25}\end{array} \)
=
\(\begin{array}{l}\frac{15-1}{25}\end{array} \)
=
\(\begin{array}{l}\frac{14}{25}\end{array} \)

B’s share =

\(\begin{array}{l}\frac{2}{5}\end{array} \)
\(\begin{array}{l}\frac{4}{25}\end{array} \)
=
\(\begin{array}{l}\frac{10-4}{25}\end{array} \)
=
\(\begin{array}{l}\frac{6}{25}\end{array} \)

New Profit Sharing Ratio = A : B : C =

\(\begin{array}{l}\frac{14}{25}\end{array} \)
:
\(\begin{array}{l}\frac{6}{25}\end{array} \)
:
\(\begin{array}{l}\frac{1}{5}\end{array} \)
=
\(\begin{array}{l}\frac{14 : 6 : 1}{25}\end{array} \)
= 14 : 6 : 1

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

\(\begin{array}{l}\frac{1}{6}\end{array} \)
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 –

\(\begin{array}{l}\frac{1}{6}\end{array} \)
\(\begin{array}{l}\frac{1}{6}\end{array} \)
=
\(\begin{array}{l}\frac{4}{6}\end{array} \)

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

X’s share =

\(\begin{array}{l}\frac{3}{5}\end{array} \)
X
\(\begin{array}{l}\frac{4}{6}\end{array} \)
=
\(\begin{array}{l}\frac{12}{30}\end{array} \)

Y’s share =

\(\begin{array}{l}\frac{2}{5}\end{array} \)
X
\(\begin{array}{l}\frac{4}{6}\end{array} \)
=
\(\begin{array}{l}\frac{8}{30}\end{array} \)

New Profit Sharing Ratio = X : Y : Z : W =

\(\begin{array}{l}\frac{12}{30}\end{array} \)
:
\(\begin{array}{l}\frac{8}{30}\end{array} \)
:
\(\begin{array}{l}\frac{1}{6}\end{array} \)
:
\(\begin{array}{l}\frac{1}{6}\end{array} \)
=
\(\begin{array}{l}\frac{12 : 8 : 5 : 5}{30}\end{array} \)
or 12 : 8 : 5 : 5

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

\(\begin{array}{l}\frac{1}{5}\end{array} \)
th profit share is admitted by C

\(\begin{array}{l}\frac{1}{6}\end{array} \)
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 –

\(\begin{array}{l}\frac{1}{5}\end{array} \)
\(\begin{array}{l}\frac{1}{6}\end{array} \)
=
\(\begin{array}{l}\frac{19}{30}\end{array} \)

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

A’s share =

\(\begin{array}{l}\frac{1}{2}\end{array} \)
X
\(\begin{array}{l}\frac{19}{30}\end{array} \)
=
\(\begin{array}{l}\frac{19}{60}\end{array} \)

B’s share =

\(\begin{array}{l}\frac{1}{2}\end{array} \)
X
\(\begin{array}{l}\frac{19}{30}\end{array} \)
=
\(\begin{array}{l}\frac{19}{60}\end{array} \)

New Profit Sharing Ratio = A : B : C : D =

\(\begin{array}{l}\frac{19}{60}\end{array} \)
:
\(\begin{array}{l}\frac{19}{60}\end{array} \)
:
\(\begin{array}{l}\frac{1}{5}\end{array} \)
:
\(\begin{array}{l}\frac{1}{6}\end{array} \)
=
\(\begin{array}{l}\frac{19 : 19 : 12 : 10}{60}\end{array} \)
or 19 : 19 : 12 : 10

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

\(\begin{array}{l}\frac{1}{4}\end{array} \)
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 –

\(\begin{array}{l}\frac{1}{4}\end{array} \)
=
\(\begin{array}{l}\frac{3}{4}\end{array} \)

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

\(\begin{array}{l}\frac{1}{2}\end{array} \)

A and B New Ratio =

\(\begin{array}{l}\frac{3}{4}\end{array} \)
X
\(\begin{array}{l}\frac{1}{2}\end{array} \)
=
\(\begin{array}{l}\frac{3}{8}\end{array} \)

New Profit Sharing Ratio = A : B : C =

\(\begin{array}{l}\frac{3}{8}\end{array} \)
:
\(\begin{array}{l}\frac{3}{8}\end{array} \)
:
\(\begin{array}{l}\frac{1}{4}\end{array} \)
=
\(\begin{array}{l}\frac{3 : 3 : 2}{8}\end{array} \)
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 =

\(\begin{array}{l}\frac{3}{5}\end{array} \)
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

\(\begin{array}{l}\frac{6}{15}\end{array} \)
:
\(\begin{array}{l}\frac{6}{20}\end{array} \)
:
\(\begin{array}{l}\frac{3}{15}\end{array} \)
:
\(\begin{array}{l}\frac{2}{10}\end{array} \)
=
\(\begin{array}{l}\frac{24 : 8 : 12 : 6}{60}\end{array} \)
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 =

\(\begin{array}{l}\frac{4}{7}\end{array} \)
\(\begin{array}{l}\frac{7}{14}\end{array} \)
=
\(\begin{array}{l}\frac{1}{14}\end{array} \)

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 =

\(\begin{array}{l}\frac{9}{20}\end{array} \)
:
\(\begin{array}{l}\frac{6}{20}\end{array} \)
:
\(\begin{array}{l}\frac{1}{4}\end{array} \)
=
\(\begin{array}{l}\frac{9 : 6 : 5}{20}\end{array} \)
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

\(\begin{array}{l}\frac{20}{100}\end{array} \)
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

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=

\(\begin{array}{l}\frac{2}{7}\end{array} \)
X
\(\begin{array}{l}\frac{3}{4}\end{array} \)
=
\(\begin{array}{l}\frac{6}{28}\end{array} \)

B’s share=

\(\begin{array}{l}\frac{5}{7}\end{array} \)
X
\(\begin{array}{l}\frac{3}{4}\end{array} \)
=
\(\begin{array}{l}\frac{15}{28}\end{array} \)

New Profit Sharing Ratio = A : B : C =

\(\begin{array}{l}\frac{6}{28}\end{array} \)
:
\(\begin{array}{l}\frac{15}{28}\end{array} \)
:
\(\begin{array}{l}\frac{1}{4}\end{array} \)
=
\(\begin{array}{l}\frac{6 : 15 : 7}{28}\end{array} \)
= 6 : 15 : 7

C’s Goodwill share distribution

C’s goodwill share = ₹ 14,000

A will receive = 14,000 X

\(\begin{array}{l}\frac{2}{7}\end{array} \)
= ₹ 4,000

B will receive = 14,000 X

\(\begin{array}{l}\frac{5}{7}\end{array} \)
= ₹ 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 =

\(\begin{array}{l}\frac{3}{5}\end{array} \)
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

Old ratio of A : B = 5 : 3

New ratio = Old ratio – Sacrificing ratio

A’s share =

\(\begin{array}{l}\frac{5}{8}\end{array} \)
\(\begin{array}{l}\frac{1}{10}\end{array} \)
=
\(\begin{array}{l}\frac{21}{40}\end{array} \)

B’s share =

\(\begin{array}{l}\frac{3}{8}\end{array} \)
\(\begin{array}{l}\frac{1}{10}\end{array} \)
=
\(\begin{array}{l}\frac{11}{40}\end{array} \)

New Profit Sharing Ratio = A : B : C =

\(\begin{array}{l}\frac{21}{40}\end{array} \)
:
\(\begin{array}{l}\frac{11}{40}\end{array} \)
:
\(\begin{array}{l}\frac{1}{5}\end{array} \)
=
\(\begin{array}{l}\frac{21 : 11: 8}{40}\end{array} \)

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

A’s goodwill share = 12,000 X

\(\begin{array}{l}\frac{1}{2}\end{array} \)
= ₹ 6,000

B’s goodwill share = 12,000 X

\(\begin{array}{l}\frac{1}{2}\end{array} \)
= ₹ 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.

10 Comments

  1. nice

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