12th | Admission of a Partner | Question No.  6 To 10 | Ts Grewal Solution 2022-2023

Old ratio of P and Q = 5:3

Share of R is 1/4th in the profits

R will take 75% From P

P will take 75% = ¾

Remaining share of Profit from Q = 1/1 - 3/4 = ¼

Sacrificing ratio of P and Q = 3:1

 

 

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.

Calculation of New Ratio

Old Ratio of Kabir and Farid 7 : 3

Kabir sacrifices his share of profit in favour of Jyoti=2/10

Farid sacrifices his share of profit in favour of Jyoti =1/10

Jyoti's Share=2/10+1/10=3/10

New Ratio = Old Share − Share Sacrificed

Kabir's New Share=7/10-2/10=5/10

Farid's New Share=3/10-1/10=2/10

New Profit Sharing Ratio = 5 : 2 : 3

Calculation of Sacrificing Ratio

Since, Kabir and Farid are sacrificing 2/10 share and 1/10 share respectively, therefore the sacrificing ratio becomes 2 : 1.

 

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 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) A, B and C are partners in the ratio of 3 : 2 : 1. D joins the firm as a new partner for 1/6th share in profits. C 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 in the ratio of 5:3. C is admitted for 3/10th share of profit half of which was gifted by A and the remaining share was taken by C equally from A and B.

 

_(i)

	R	T
OLD RATION	3  :	2  :

Sacrificing Ratio = Old Ratio × Surrender Ratio

R’s=3/5×1/4=3/20

T’s=2/5×1/5=2/25

 

New Ratio = Old Ratio − Sacrificing Ratio

R= 3/5-3/20=9/20

T=2/5-2/25=8/25

 

S’s Share = R’s Sacrifice + S’s Sacrifice

=3/20+2/25=23/100

	R		T		S
New profit sharing ratio =	9/20	:	8/25	:	23/100
=	25/100	:	32/100	:	23/100
=	25	:	32	:	23

(ii)

	A	B
OLD RATION	1  :	1

C admits for 1/4^th share of profit

Let the combined share of A, B and C be = 1

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

=1-1/4=3/4

New Ratio = Combined share of A and B ×2/3

A’s=3/4×2/3=6/12

B’s=3/4×1/3=3/12

	A		B		C
New profit sharing ratio =	6/12	:	3/12	:	¼
=	6/12	:	3/12	:	3/12
=	2	:	1	:	1

 

(iii)

	A	B
OLD RATION	3 :	2

            C admits for 1/5share of profit

A’s sacrifice	= C’s share× 1/5
	=1/5×1/5
	=1/25
B’s sacrifice	= C’s share× 4/5
	=1/5×4/5
	=4/25

New Ratio = Old Ratio − Sacrificing Ratio

A’s =3/5-1/25=14/25

B’s=2/5-4/25=6/25

	A		B		C
New profit sharing ratio =	14/25	:	6/25	:	1/5
=	14/25	:	6/25	:	5/25
=	14	:	6	:	5

(iv)

	X	Y	Z
OLD RATION	3  :	2  :	1

W admits for 1/6         share of profit

Let combined share of all partner after W’s admission be = 1

Combined share X and Y in the new firm =1- Z’s share- W’s share

=1-1/6-1/6

=4/6

New Ratio = Old Ratio × Combined share of X and Y

A’s

=3/5×4/6

=12/30

B’s

=2/5×4/6

=8/30

X

Y

Z

W

New profit sharing ratio =

12/30

:

8/30

:

1/6

:

1/6

=

12/30

:

8/30

:

5/30

:

5/30

=

12

:

8

:

5

:

5

(v)

	A	B
OLD RATION	1  :	1

C admits for 1/5 share

D admits for 1/6 share

Let combined share of all partner after C and D’s admission be = 1

Combined share of profit of A and B after C and D’s admission =1- C’s share- Z’s share

=1-1/5-1/6

=19/30

New Ratio = Old Ratio × Combined share of A and B

A’s

=1/2×19/30

=19/60

B’s

=1/2×19/30

=19/60

X

Y

Z

W

New profit sharing ratio =

19/60

:

19/60

:

1/5

:

1/6

=

19/60

:

19/60

:

12/60

:

10/60

=

19

:

19

:

12

:

10

(vi)

A and B are partners sharing profits in the ratio of 5:3

C’s share is  3/10^th

Gift by A to C = 3/10 ×1/2=3/20

Remaining half taken by C from A and B Equally

From A and B = 3/20 × ½ = 3/40

Given by A in total = 3/20+ 3/40=6+3/40=9/40

Remaining Share of A and B

A= 5/8-9/40=25-9/40=16/40

B= 3/8-3/40=15-3/40=12/40

New Ratio of A , B and C

= 16/40 : 12/40 : 3/10

= 4 : 3 :3