Old ratio of Praveena and Dhanya = 7:3 that is \(\frac{7}{10}:\frac{3}{10}\)
New ratio of Paveena, Dhanya and Malini = 5:2:3 that is, \(\frac{5}{10};\frac{2}{10};\frac{3}{10}\)
Share sacrificed = Old share - New share
Praveena \(=\frac { 7 }{ 10 } -\frac { 5 }{ 10 } =\frac { 7-5 }{ 10 } =\frac { 2 }{ 10 } \)
Dhanya \(=\frac { 3 }{ 10 } -\frac { 2 }{ 10 } =\frac { 3-2 }{ 10 } =\frac { 1 }{ 10 } \)
Sacrificing ratio ofPraveena and Dhanya is \(\frac { 2 }{ 10 } :\frac { 1 }{ 10 } \) that is 2:1

Adjustment for goodwill
As the sacrifice made by the existing partners is not mentioned, it is assumed that they sacrifice in their old profit sharing ratio 3 : 2.

Journal Entry

Date	Particulars	L.F	Debit Rs.	Credit Rs.
	Bank A/c		10,000
	To Aaparna's capital A/c (3/5)			6,000
	To Priya's Capital A/c (2/5)			4,000
	(Cash brought for goodwill credited to Aparna's and Priya in sacrificing ratio)
	Apama's capital A/c       Dr		6,000
	Priya's Capital A/c          Dr		4,000
	To Bank A/c			10,000
	(Amount withdrawn by the partners)

Computation of sacrificing ratio and new profit sharing ratio
Old ratio of Ambika, Dharani and Padma \(5:3:2\quad or\quad \frac { 5 }{ 10 } :\frac { 3 }{ 10 } :\frac { 2 }{ 10 } \)
Ramya's share of profit = 25% or \(\frac { 25 }{ 100 } or\frac { 1 }{ 4 } \)
Let the total share be 1 
Remaining share \(=1-\frac { 1 }{ 4 } =\frac { 4-1 }{ 4 } =\frac { 3 }{ 4 } \)
New share of old partners = Remaining share \(\times\) Old share
Ambika \(=\frac { 3 }{ 4 } \times \frac { 5 }{ 10 } =\frac { 15 }{ 40 } \)
Dharani \(=\frac { 3 }{ 4 } \times \frac { 3 }{ 10 } =\frac { 9 }{ 40 } \)
Padma \(=\frac { 3 }{ 4 } \times \frac { 2 }{ 10 } =\frac { 6 }{ 40 } \)
Share of new partner
Ramya \(=\frac { 1 }{ 4 } \)
In order to equalise the denominator, multiply and divide Ramya's share by 10 
Rarnyas share \(=\frac { 1 }{ 4 } \times \frac { 10 }{ 10 } =\frac { 10 }{ 40 } \)
New profit sharing ratio of Ambika, Dharani, Padma and Ramya \(=\frac { 15 }{ 40 } :\frac { 9 }{ 40 } :\frac { 6 }{ 40 } :\frac { 10 }{ 40 } \), that is 15: 9: 6: 10

Computation of sacrificing ratio and new profit sharing ratio
Since share sacrificed, proportion of share sacrificed and new profit sharing ratio are not given, it is assumed that the existing partners sacrifice in their old profit sharing ratio, that is 3 : 2
Sacrificing ratio of Mala and Anitha is 3 : 2
Let the total share be 1
Mercy's share =\(\frac{1}{5}\)
Remaining share \(=1-\frac { 1 }{ 5 } =\frac { 5-1 }{ 5 } =\frac { 4 }{ 5 } \)
New share of old partners = Remaining share \(\times\) Old share
Mala \(=\frac { 4 }{ 5 } \times \frac { 3 }{ 5 } =\frac { 12 }{ 25 } \)
Anitha \(=\frac { 4 }{ 5 } \times \frac { 2 }{ 5 } =\frac { 8 }{ 25 } \)
Share of New partner
Mercy \(\frac{1}{5}\)
In order to equalise the denominator, multiply and divide by 5
Mercy's share \(=\frac { 1 }{ 5 } \times \frac { 5 }{ 5 } =\frac { 5 }{ 25 } \)
New profit sharing ratio of Mala, Anitha and Mercy \(=\frac { 12 }{ 25 } :\frac { 8 }{ 25 } :\frac { 5 }{ 25 } \), that is 12:8:5

Computation of sacrificing ratio and new profit sharing ratio
Siva's share = \(\frac{1}{5}\)
Proportion of share sacrificed = 1 : 1 (equally) i.e.\(\frac{1}{2}:\frac{1}{2}\)
Share scarified = New partner's share x Proportion of share sacrificed
Selvam \(=\frac { 1 }{ 5 } \times \frac { 1 }{ 2 } =\frac { 1 }{ 10 } \)
Senthil \(=\frac { 1 }{ 5 } \times \frac { 1 }{ 2 } =\frac { 1 }{ 10 } \)
Sacrificing ratio of Selvam and Senthil is \(\frac { 1 }{ 10 } :\frac { 1 }{ 10 } \) that is 1:1
New share of old partner = Old share - Share sacrificed
Selvam \(=\frac { 2 }{ 5 } -\frac { 1 }{ 10 } =\frac { 4-1 }{ 10 } =\frac { 3 }{ 10 } \)
Senthil \(=\frac { 3 }{ 5 } -\frac { 1 }{ 10 } =\frac { 6-1 }{ 10 } =\frac { 5 }{ 10 } \)
Share of new partner
Siva = \(\frac{1}{5}\)
In order to equate, monthly and divide Siva's share by 2
\(=\frac { 1 }{ 5 } \times \frac { 2 }{ 2 } =\frac { 2 }{ 10 } \)
New profit sharing ratio of Selvam, Senthil and Siva \(=\frac { 3 }{ 10 } :\frac { 5 }{ 10 } :\frac { 2 }{ 10 } \), that is 3:5:2

Computation of sacrificing ratio and new profit sharing ratio
Kailash's share = \(\frac {1}{4}\)
Old ratio = 1:1 that is \(\frac { 1 }{ 2 } :\frac { 1 }{ 2 } \)
Proportion of share sacrificed 7 : 3 that is  \(\frac { 7 }{ 10 } :\frac { 3 }{ 10 } \)
Share scarified = New partner's share x Proportion of share sacrificed
Karthik \(=\frac { 1 }{ 4 } :\frac { 7 }{ 10 } =\frac { 7 }{ 10 } \)
Kannan \(=\frac { 1 }{ 4 } \times \frac { 3 }{ 10 } =\frac { 3 }{ 40 } \)
Sacrificing ratio of Karthik and Kannan is \(\frac { 7 }{ 10 } \) and \(\frac { 3 }{ 10 } \) that is 7:3
New share of old partner = Old share - Share sacrificed
Karthik \(=\frac { 1 }{ 2 } -\frac { 7 }{ 40 } =\frac { 20-7 }{ 40 } =\frac { 13 }{ 40 } \)
Kannan \(=\frac { 1 }{ 2 } -\frac { 3 }{ 40 } =\frac { 20-3 }{ 40 } =\frac { 17 }{ 40 } \)
Share of new partner Kailash =\(\frac{1}{4}\)
In order to equate the denominator, multiply and divide Kailash's share by 10 \(=\frac { 1 }{ 4 } \times \frac { 10 }{ 10 } =\frac { 10 }{ 40 } \)
Thus, the New profit sharing ratio \(=\frac { 13 }{ 40 } :\frac { 17 }{ 40 } :\frac { 10 }{ 40 } \) =13:17:10

Computation of sacrificing ratio and new profit sharing ratio
Old share = 5:3 that is prema \(\frac{5}{8}\) amd Chandra \(\frac{3}{8}\)
Share scarified =Old share x Proportion of share sacrificed
Prema \(=\frac { 5 }{ 8 } \times \frac { 1 }{ 8 } =\frac { 5 }{ 64 } \)
Chandra \(=\frac { 3 }{ 8 } \times \frac { 1 }{ 8 } =\frac { 3 }{ 64 } \)
Sacrificing ratio of Prema and Chandra is \(\frac{5}{64}\)and \(\frac{3}{64}\) that is 5:3
New share = Old share - Share sacrificed
Prema \(=\frac { 5 }{ 8 } -\frac { 5 }{ 64 } =\frac { 40-5 }{ 64 } =\frac { 35 }{ 64 } \)
Chandra \(=\frac { 3 }{ 8 } -\frac { 3 }{ 64 } =\frac { 24-3 }{ 64 } =\frac { 21 }{ 64 } \)
Share of new partner = Sum of shares sacrificed by Prema and Chandra
Hema \(=\frac { 5 }{ 24 } +\frac { 3 }{ 64 } =\frac { 5+3 }{ 64 } =\frac { 8 }{ 64 } \)
New profit sharing ratio of Prema, Chandra and Hema \(=\frac { 35 }{ 64 } :\frac { 21 }{ 64 } :\frac { 8 }{ 64 } \), that is 35:21:8

Computation of sacrificing ratio and new profit sharing ratio
Old share = 5 : 4 that is, Govind \(\frac{5}{9}\) and Gopal \(\frac{4}{9}\)
Share scarified = Old share \(\times\) Proportion of share sacrificed
Govind \(=\frac { 5 }{ 9 } \times \frac { 2 }{ 9 } =\frac { 10 }{ 81 } \)
Gopal \(=\frac { 4 }{ 9 } \times \frac { 1 }{ 9 } =\frac { 4 }{ 81 } \)
Sacrificing ratio of Govind and Gopal is \(\frac{10}{81}\) and \(\frac{4}{81}\), that is 10:4 or 5:2
New share =Old share - Share sacrificed
Govind \(=\frac { 5 }{ 9 } -\frac { 10 }{ 81 } =\frac { 45-10 }{ 81 } =\frac { 35 }{ 81 } \)
Gopal = \(=\frac { 4 }{ 9 } -\frac { 4 }{ 81 } =\frac { 36-4 }{ 81 } =\frac { 32 }{ 81 } \)
Share of new partner = Sum of shares sacrificed by Govind and Gopal
Rahim \(=\frac { 10 }{ 81 } +\frac { 4 }{ 81 } =\frac { 10+4 }{ 81 } =\frac { 14 }{ 81 } \)
New profit sharing ratio of Govind, Gopal and Rahim \(=\frac { 35 }{ 81 } :\frac { 32 }{ 81 } :\frac { 14 }{ 81 } \), that is 35: 32: 14

Computation of sacrificing ratio and new profit sharing ratio
Share sacrificed \(=\frac{1}{14}:\frac{1}{14}\)
Sacrificing ratio of Vimala and Kamala is 1 : 1
Old ratio is 4: 3 that is \(\frac { 4 }{ 7 } :\frac { 3 }{ 7 } \)
New share of old partner = Old share - Share sacrificed
Vimala \(=\frac { 4 }{ 7 } -\frac { 1 }{ 14 } =\frac { 8-1 }{ 14 } =\frac { 7 }{ 14 } \)
Kamala \(=\frac { 3 }{ 7 } -\frac { 1 }{ 14 } =\frac { 6-1 }{ 14 } =\frac { 5 }{ 14 } \)
Share of new partner:
Vinitha = Sum of shares sacrificed by old partners
\(=\frac { 1 }{ 14 } +\frac { 1 }{ 14 } =\frac { 2 }{ 14 } \)
New profit sharing ratio of Vimala, Kamala and Vinitha is \(\frac { 7 }{ 14 } :\frac { 5 }{ 14 } :\frac { 2 }{ 14 } \) or 7:5:2

Computation of sacrificing ratio and new profit sharing ratio
Share sacrificed \(=\frac { 1 }{ 20 } :\frac { 4 }{ 20 } \)
Sacrificing ratio of Raja and Ravi is 1 : 4
Old profit sharing ratio = \(3:2\quad or\quad \frac { 3 }{ 5 } :\frac { 2 }{ 5 } \)
New share of old partners = Old share - Share sacrificed
Raja  \(=\frac { 3 }{ 5 } -\frac { 1 }{ 20 } =\frac { 12-1 }{ 20 } =\frac { 11 }{ 20 } \)
Ravi \(=\frac { 2 }{ 5 } -\frac { 4 }{ 20 } =\frac { 8-4 }{ 20 } =\frac { 4 }{ 20 } \)
Share of new partner Ram = \(\frac{1}{4}\)
In order to equate the denominator of Ram's share, multiply and divide by 5 
\(=\frac { 1 }{ 4 } \times \frac { 5 }{ 5 } =\frac { 5 }{ 20 } \)
New profit sharing ratio of Raja, Ravi and Ram \(=\frac { 11 }{ 20 } :\frac { 4 }{ 20 } :\frac { 5 }{ 20 } \)
= 11 : 4 : 5

Computation of sacrificing ratio and new profit sharing ratio
Share sacrificed by old partners 
Ananth = \(\frac{1}{5}\)
Suman = 0
Sacrificing ratio = 1 : 0
Old profit of Ananth and Suman is 3 : 2 that is \(\frac { 3 }{ 5 } :\frac { 2 }{ 5 } \)
New share of old partner = Old share - Share sacrificed
Ananth \(=\frac { 3 }{ 5 } -\frac { 1 }{ 5 } =\frac { 3-1 }{ 5 } =\frac { 2 }{ 5 } \)
Suman = \(\frac { 2 }{ 5 } \)
Share of new partner Saran = \(\frac { 1 }{ 5 } \)
New profit sharing ratio of Ananth, Suman and saran is \(\frac { 2 }{ 5 } :\frac { 2 }{ 5 } :\frac { 1 }{ 5 } \) that is 2:2:1

Journal Entry

Date	Particulars	L.F	Debit Rs.	Credit Rs.
2019 Apr 1	Profit and loss appropriation A/c           Dr		40,000
	General reserve A/c                                 Dr		8,000
	Workmen's compensation fund A/c     Dr		12,000
	To Oviya's capital A/c(60,000 × 5/8)			37,500
	To Kaviyas capital A/c(60,000 × 3/8)			22,500
	(Accumulated profit and reserve transferred to Old partner's capital account in the old profit staring ratio)

Journal Entry

Date	Particulars	L.F	Debit Rs.	Credit Rs.
2018 January 1	Anjali's capital A/c (40,000\(\times\)5/8)    Dr		25,000
	Nithya's capital A/c (40,000 \(\times\) 3/8) Dr		15,000
	To Profit and loss A/c			40,000
	(Accumulated loss transferred to old partner's capital account in the old profit sharing ratio)

Journal Entry

Date	Particulars	L.F	Debit Rs.	Credit Rs.
2018 March 31	General reserve A/c                                        Dr		42,000
	To AruI's capital A/c \(\left( 42,000\times \frac { 4 }{ 7 } \right) \)			24,000
	To Anita's capital A/ c \(\left( 42,000\times \frac { 3 }{ 7 } \right) \)			18,000
	(General reserve transferred to old partner's capital account in the old profit sharing ratio)

(a) Debit account
(b) Debit account
(c) Debit account
(d) Credit account

Jourbal Entry

Date	Particular	L.F	Debit Rs.	Credit Rs.
	Old partner's capital/current Ale (in old ratio) Dr		xxx
	To goodwill A/c			xxx
	(Existing goodwill written off)

Sacrificing ratio is the proportion of the profit which is sacrificed or foregone by the old partners in favour of the new partner. The purpose of finding the sacrificing ratio is to share the goodwill brought in by the new partner. 
Share sacrificed = Old share - New share
Sacrificing ratio = Ratio of share sacrificed by the old partners

Profits and losses of previous years which are not distributed to the partners are called accumulated profit and losses. Any reserve and accumulated profits and losses belong to the oldpartners and hence these should be distributed to the old partners in the old profit sharing ratio.

When a partner is admitted into the partnership, the assets and liabilities are revalued as the current value may differ from the book value. Determination of current values of assets and liabilities is called revaluation of assets and liabilities.

Calculation of sacrificing ratio
Sacrificing ratio = Old share – New share
Aravind = \(\frac { 3 }{ 5 } -\frac { 1 }{ 3 } =\frac { 9-5 }{ 15 } =\frac { 4 }{ 15 } \)
Balaji = \(\frac { 2 }{ 5 } -\frac { 1 }{ 3 } =\frac { 6-5 }{ 15 } =\frac { 1 }{ 15 } \)
Therefore, sacrificing ratio is 4:1

Journal entry

Date	Particulars		L.F.	Debit Rs.	Credit Rs.
	Cash A/c	Dr.		12,000
	Anirudh’s capital A/c	Dr.		8,000
	To Aravind’s capital A/c (4/5)				16,000
	To Balaji’s capital A/c (1/5) (Share of goodwill of Anirudh credited to old partners’ capital account)				4,000

As the sacrifice made by the existing partners is not mentioned, it is assumed that they sacrifice
in their old profit sharing ratio of 5:1. Therefore, sacrificing ratio is 5:1.
Tharun’s share of goodwill = 27,000 \(\times\) \(\frac { 2 }{ 9 } \) = Rs. 6,000

Journal entry

Date	Particulars		L.F.	Debit Rs.	Credit Rs.
	Tharun’s capital A/c	Dr.		6,000
	To Ashok’s capital A/c (5/6)				5,000
	To Mumtaj’s capital A/c (1/6) (Tharun’s share of goodwill credited to the old partners’ capital account in the sacrificing ratio)				1,000

Calculation of sacrificing ratio
Sacrificing ratio = Old share – New share
Vasu = \(\frac { 3 }{ 5 } -\frac { 3 }{ 8 } =\frac { 24-15 }{ 40 } =\frac { 9 }{ 40 } \)
Devi = \(\frac { 2 }{ 5 } -\frac { 3 }{ 8 } =\frac { 16-15 }{ 40 } =\frac { 1 }{ 40 } \)
Therefore, sacrificing ratio is 9:1

Journal entry

Date	Particulars		L.F.	Debit Rs.	Credit Rs.
	Bank A/c	Dr.		3,000
	To Vasu’s current A/c (9/10)				2,700
	To Devi’s current A/c (1/10) (Cash brought for goodwill credited to old partners’ capital account in sacrificing ratio)				300

Durai’s share of goodwill = 36,000 × 1/4 = Rs. 9,000
As the sacrifice made by the existing partners is not mentioned, it is assumed that they sacrifice in their old profit sharing ratio 1:1:1. Therefore, sacrificing ratio is 1:1:1.

Journal Entries

Date	Particulars		L.F.	Debit Rs.	Credit Rs.
	Bank A/c	Dr..		9,000
	To Arun’s capital A/c				3,000
	To Babu’s capital A/c				3,000
	To Charles’s capital A/c (Cash brought for goodwill credited to old partners’ capital account in sacrificing ratio)				3,000
	Arun’s capital A/c	Dr.		1,500
	Babu’s capital A/c			1,500
	Charles’s capital A/c			1,500
	To Bank A/c (Cash withdrawn by the partners				4,500

As the sacrifice made by the existing partners is not mentioned, it is assumed that they sacrifice in their old profit sharing ratio 5:3. Therefore, sacrificing ratio is 5:3.

Journal Entry

Date	Particulars		L.F.	Debit Rs.	Credit Rs.
2019		Dr..		8,000
January 1	To Amudha’s capital A/c (5/8)				5,000
	To Bhuvana’s capital A/c (3/8) (Cash brought for goodwill credited to Amudha and Bhuvana in sacrificing ratio)				3,000
	Amudha’s capital A/c	Dr.		5,000
	Bhuvana’s capital A/c	Dr.		3,000
	To Bank A/c (Amount withdrawn by the partners)				8,000

Computation of sacrificing ratio and new profit sharing ratio
Old ratio of Anil, Sunil and Hari = 4 : 3 : 3 or \(\frac { 4 }{ 10 } :\frac { 3 }{ 10 } :\frac { 3 }{ 10 } \)
Raja’s share of profit = 20% or 20/100 or 1/5
Let the total share be 1
Remaining share =  \(1-\frac { 1 }{ 5 } =\frac { 5-1 }{ 5 } \)
= \(\frac { 4 }{ 5 } \)
New share of old partners = Remaining share × Old share
Anil = \(\frac { 4 }{ 5 } \times \frac { 1 }{ 10 } =\frac { 16 }{ 50 } \)
Sunil = \(\frac { 4 }{ 5 } \times \frac { 3 }{ 10 } =\frac { 12 }{ 50 } \)
Hari =  \(\frac { 4 }{ 5 } \times \frac { 3 }{ 10 } =\frac { 12 }{ 50 } \)
Share of new partner Raja =  \(\frac { 1 }{ 5 } \)
In order to equalise the denominator, multiply and divide Raja’s share by 10
Raja’s share = \(\frac { 1 }{ 5 } \times \frac { 10 }{ 10 } =\frac { 10 }{ 50 } \)
New profit sharing ratio of Anil, Sunil, Hari and Raja = \(\frac { 16 }{ 50 } :\frac { 12 }{ 50 } :\frac { 12 }{ 50 } :\frac { 12 }{ 50 } \) that is, 8 : 6 : 6 : 5.

Computation of sacrificing ratio and new profit sharing ratio:
Since share sacrificed, proportion of share sacrificed and new profit sharing ratio are not given, it is assumed that the existing partners sacrifice in their old profit sharing ratio, that is, 2:1. Sacrificing ratio of Vimal and Athi is 2:1
Let the total share be 1
Jeyam’s share = \(\frac { 1 }{ 4 } \)
Remaining share =  \(1-\frac { 1 }{ 4 } =\frac { 4-1 }{ 4 } \)
= \(\frac { 3 }{ 4 } \)
New share of old partners = Remaining share × Old share
Vimal = \(\frac { 3 }{ 4 } \times \frac { 2 }{ 3 } =\frac { 6 }{ 12 } \)
Athi = \(\frac { 3 }{ 4 } \times \frac { 1 }{ 3 } =\frac { 3 }{ 12 } \)
Share of new partner Jeyam = \(\frac { 1 }{ 4 } \)
In order to equalise the denominator, multiply and divide by 3
Jeyam’s share = \(\frac { 1 }{ 4 } \times \frac { 3 }{ 3 } =\frac { 3 }{ 12 } \)
New profit sharing ratio of Vimal,  Athi and Jeyam = \(\frac { 6 }{ 12 } :\frac { 3 }{ 12 } :\frac { 3 }{ 12 } \) that is, 2 : 1 : 1.

Computation of sacrificing ratio and new profit sharing ratio
Arun’s share = \(\frac { 1 }{ 4 } \)
Proportion of share sacrificed = 1:1(equally) i.e. \(\frac { 1 }{ 2 } :\frac { 1 }{ 2 } \)
Share sacrificed = New partner’s share × Proportion of share sacrificed
Mahesh = \(\frac { 1 }{ 4 } \times \frac { 1 }{ 2 } =\frac { 1 }{ 8 } \)
Dhanush = \(\frac { 1 }{ 4 } \times \frac { 1 }{ 2 } =\frac { 1 }{ 8 } \)
Sacrificing ratio of Mahesh and Dhanush is \(\frac { 1 }{ 8 } :\frac { 1 }{ 8 } \) that is, 1:1
New share of old partner = Old share - Share sacrificed
Mahesh = \(\frac { 2 }{ 3 } -\frac { 1 }{ 8 } =\frac { 16-3 }{ 24 } =\frac { 13 }{ 24 } \)
Dhanush = \(\frac { 1 }{ 3 } -\frac { 1 }{ 8 } =\frac { 8-3 }{ 24 } =\frac { 5 }{ 24 } \)
Share of new partner Arun = \(\frac { 1 }{ 4 } \)
In order to equate, multiply and divide Arun’s share by 6
= \(\frac { 1 }{ 4 } \times \frac { 6 }{ 6 } =\frac { 6 }{ 24 } \)
New profit sharing ratio of Mahesh, Dhanush and Arun = \(\frac { 13 }{ 24 } :\frac { 5 }{ 24 } :\frac { 6 }{ 24 } \)that is, 13:5:6.

Computation of sacrificing ratio and new profit sharing ratio
Ranjan’s share = \(\frac { 1 }{ 4 } \)
Old ratio=2:1 that is, \(\frac { 2 }{ 3 } :\frac { 1 }{ 3 } \)
Proportion of share sacrificed = 3:2 that is, \(\frac { 3 }{ 5 } :\frac { 2 }{ 5 } \)
Share sacrificed = New partner’s share × Proportion of share sacrificed
Ramesh = \(\frac { 1 }{ 4 } \times \frac { 3 }{ 5 } =\frac { 3 }{ 20 } \)
Raju = \(\frac { 1 }{ 4 } \times \frac { 2 }{ 5 } =\frac { 2 }{ 20 } \)
Sacrificing ratio of Ramesh and Raju is \(\frac { 3 }{ 20 } \) and \(\frac { 2 }{ 20 } \), that is, 3:2
New share of old partner = Old share - Share sacrificed
Ramesh = \(\frac { 2 }{ 3 } -\frac { 3 }{ 20 } =\frac { 40-9 }{ 60 } =\frac { 31 }{ 60 } \)
Raju = \(\frac { 1 }{ 3 } -\frac { 2 }{ 20 } =\frac { 20-6 }{ 60 } =\frac { 14 }{ 60 } \)
Share of new partner Ranjan = \(\frac { 1 }{ 4 } \)
In order to equate the denominator, multiply and divide Ranjan’s share by 15
= \(\frac { 1 }{ 4 } \times \frac { 15 }{ 15 } =\frac { 15 }{ 60 } \)
Thus, the new profit sharing ratio = \(\frac { 31 }{ 60 } :\frac { 14 }{ 60 } :\frac { 15 }{ 60 } \) = 31 : 14 : 15

Computation of sacrificing ratio and new profit sharing ratio
Old share = 3:2 that is, Prasanth \(\frac { 3 }{ 5 } \) and Nisha \(\frac { 2 }{ 5 } \)
Share sacrificed = Old share × Proportion of share sacrificed
Prasanth = \(\frac { 3 }{ 5 } \times \frac { 2 }{ 5 } =\frac { 6 }{ 25 } \)
Nisha = \(\frac { 2 }{ 5 } \times \frac { 2 }{ 5 } =\frac { 4 }{ 25 } \)
Sacrificing ratio of Prasanth and Nisha is \(\frac { 6 }{ 25 } \) and \(\frac { 4 }{ 25 } \), that is, 3:2
New share = Old share - Share sacrificed
Prasanth = \(\frac { 3 }{ 5 } -\frac { 6 }{ 25 } =\frac { 15-6 }{ 25 } =\frac { 9 }{ 25 } \)
Nisha = \(\frac { 2 }{ 5 } -\frac { 4 }{ 25 } =\frac { 10-4 }{ 25 } =\frac { 6 }{ 25 } \)
Share of new partner = Sum of shares sacrificed by Prasanth and Nisha
Ramya = \(\frac { 6 }{ 25 } +\frac { 4 }{ 25 } =\frac { 6+4 }{ 25 } =\frac { 10 }{ 25 } \)
New profit sharing ratio of Prasanth, Nisha and Ramya = \(\frac { 9 }{ 25 } :\frac { 6 }{ 25 } :\frac { 10 }{ 25 } \) that is, 9:6:10

Computation of sacrificing ratio and new profit sharing ratio
Old share = 3:2 that is, Suresh \(\frac { 3 }{ 5 } \) and Dinesh \(\frac{2}{5}\) \(Suresh\)
Share sacrificed = Old share x Proportion of share sacrificed
Suresh = \(\frac { 3 }{ 5 } \times \frac { 1 }{ 5 } =\frac { 3 }{ 25 } \)
Dinesh = \(\frac { 2 }{ 5 } \times \frac { 2 }{ 5 } =\frac { 4 }{ 25 } \)
Sacrificing ratio of Suresh and Dinesh is \(\frac { 3 }{ 25 } \) and \(\frac { 4 }{ 25 } \) that is, 3:4
New share = Old share - Share sacrificed
Suresh = \(\frac { 3 }{ 5 } -\frac { 3 }{ 25 } =\frac { 15-3 }{ 25 } =\frac { 12 }{ 25 } \)
Dinesh = \(\frac { 2 }{ 5 } -\frac { 4 }{ 25 } =\frac { 10-4 }{ 25 } =\frac { 6 }{ 25 } \)
Share of new partner = Sum of shares sacrificed by Suresh and Dinesh
Ramesh = \(\frac { 3 }{ 25 } +\frac { 4 }{ 25 } =\frac { 3+4 }{ 25 } =\frac { 7 }{ 25 } \)
New profit sharing ratio of Suresh, Dinesh and Ramesh = \(\frac { 12 }{ 25 } :\frac { 6 }{ 25 } :\frac { 7 }{ 25 } \)that is, 12:6:7.

Computation of sacrificing ratio and new profit sharing ratio
Share sacrificed =  \(\frac { 1 }{ 5 } ,\frac { 1 }{ 5 } \)
Sacrificing ratio of Hameed and Govind is 1:1
Old ratio is 5:3 that is \(\frac { 5 }{ 8 } :\frac { 3 }{ 8 } \)
New share of old partner = Old share - Share sacrificed
Hameed = \(\frac { 5 }{ 8 } -\frac { 1 }{ 5 } =\frac { 25-8 }{ 40 } =\frac { 17 }{ 40 } \)
Govind = \(\frac { 3 }{ 8 } -\frac { 1 }{ 5 } =\frac { 15-8 }{ 40 } =\frac { 7 }{ 40 } \)
Share of new partner
John = Sum of shares sacrificed by old partners
=\(\frac { 1 }{ 5 } +\frac { 1 }{ 5 } =\frac { 2 }{ 5 } \)
In order to equalise the denominator of John’s share, multiply and divide by 8 John’s share =\(\\ \frac { 2 }{ 5 } \times \frac { 8 }{ 8 } =\frac { 16 }{ 40 } \)
New profit sharing ratio of Hameed, Govind and John is \(\frac { 17 }{ 40 } :\frac { 7 }{ 40 } :\frac { 16 }{ 40 } \) or 17:7:16

Computation of sacrificing ratio and new profit sharing ratio
Shares sacrificed = \(\frac { 2 }{ 7 } ,\frac { 1 }{ 7 } \)
Sacrificing ratio of Ravi and Kumar is 2:1
Old profit sharing ratio = 7:3 or \(\frac { 7 }{ 10 } :\frac { 3 }{ 10 } \)
New share of old partners = Old share - Share sacrificed
Ravi = \(\frac { 7 }{ 10 } -\frac { 2 }{ 7 } =\frac { 49-20 }{ 70 } =\frac { 29 }{ 70 } \)
Kumar = \(\frac { 3 }{ 10 } -\frac { 1 }{ 7 } =\frac { 21-10 }{ 70 } =\frac { 11 }{ 70 } \)
Share of new partner Christy = \(\frac { 3 }{ 7 } \)
In order to equate the denominator of Christy’s share, multiply and divide by 10
= \(\frac { 3 }{ 7 } \times \frac { 10 }{ 10 } =\frac { 30 }{ 70 } \)
New profit sharing ratio of Ravi, Kumar and Christy = \(\frac { 29 }{ 70 } :\frac { 11 }{ 70 } :\frac { 30 }{ 70 } \) = 29:11:30

Computation of sacrificing ratio and new profit sharing ratio
Share sacrificed by old partners
Hari =\(\frac { 1 }{ 8 } \)
Saleem = 0
Sacrificing ratio = 1:0
Old ratio of Hari and Saleem is 5:3 that is \(\frac { 5 }{ 8 } :\frac { 3 }{ 8 } \)
New share of old partner = Old share - Share sacrificed
Hari = \(\frac { 5 }{ 8 } -\frac { 1 }{ 8 } =\frac { 5-1 }{ 8 } =\frac { 4 }{ 8 } \)
Saleem = \(\frac { 3 }{ 8 } \)
Share of new partner Joel = \(\frac { 1 }{ 8 } \)
New profit sharing ratio of Hari, Saleem and Joel is \(\frac { 4 }{ 8 } :\frac { 3 }{ 8 } :\frac { 1 }{ 8 } \) that is, 4:3:1.

Old ratio of Anbu and Raju = 3:2 that is, \(\frac { 3 }{ 5 } :\frac { 2 }{ 5 } \)
New ratio of Anbu, Raju and Akshai = 5:3:2, that is, \(\frac { 5 }{ 10 } :\frac { 3 }{ 10 } :\frac { 2 }{ 10 } \)
Share sacrificed = Old share - New share
Anbu = \(\frac { 3 }{ 5 } -\frac { 5 }{ 10 } =\frac { 6-5 }{ 10 } =\frac { 1 }{ 10 } \)
Raju =  \(\frac { 2 }{ 5 } -\frac { 3 }{ 10 } =\frac { 4-3 }{ 10 } =\frac { 1 }{ 10 } \)
Sacrificing ratio of Anbu and Raju is \(\frac { 1 }{ 10 } :\frac { 1 }{ 10 } \) that is 1:1

Journal entry

Date	Particulars		L.F.	Debit Rs.	Credir Rs.
2017	Profit and loss appropriation A/c	Dr.		20,000
April 1	General reserve A/c	Dr.		5,000
	Workmen compensation fund A/c	Dr.		15,000
	To Rathna Kumar’s capital A/c (40,000 \(\times\) 3/5)				24,000
	To Arockia Das’s capital A/c (40,000 \(\times\) 2/5)				16,000
	(Accumulated profit and reserve transferred to old partners’ capital account in the old profit sharing ratio)

Journal entry

Date	Particulars	L.E.	Debit Rs.	Credit Rs.
2019	Kavitha’s capital A/c Dr.		40,000
January 1	Radha’s capital A/c Dr.		30,000
	To Profit and loss a/c (Accumulated loss transferred to old partners’ capital account in the old profit sharing ratio)			70,000

Journal entry

Date	Particulars	L.E.	Debit Rs.	Credit Rs.
2017	Reserve fund A/c Dr.		50,000
March 31	To Mala’s capital A/c (50,000 \(\times\) 3/5)			30,000
	To Vimala’s capital A/c (50,000 \(\times\) 2/5) (Reserve fund transferred to old partners’ capital account in the old profit sharing ratio)			20,000