Page No 5.86:

Question 6:

X and Y are partners in a firm sharing profits and losses in the ratio of 3 : 2. Z is admitted as partner with 1/4 share in profit. Z takes his share from X and Y in the ratio of 2 : 1. Calculate new profit-sharing ratio.

Answer:

Old Profit Sharing Ratio amongst Partners (X and Y) is 3 : 2
Z is admitted for 1/4^th Share in Profits
Sacrificing Ratio of X and Y is 2 : 1
Z aquires =2/3×1/4=2/12 from X

Z aquires =1/3×1/4=1/12 from Y

New ratio= old ratio – new ratio

X‘s new share=3/5 -2/12 =36-10/60=26/60

Y‘s new share=2/5 -1/12 =24-5/60=19/60

Z’s share=1/4=15/60

New ratio= 26:19:15

Page No 5.86:

Question 7:

Old ratio: S:J:B=1:1:1

T is admitted for 1/5 share

Let the total Profit of firm be 1

Remaining share of the SJB after T’s admission = 1-1/5=5-1/5=4/5

New share

S=4/5×1/3=4/15

T=1/5×3/3=3/15

New profit sharing ratio of all partners S:J:B:T = 4:4:4:3

Sacrificing ratio= Old – new

S=1-3-4/15=5-4/15=1/15

J=1-3-4/15=5-4/15=1/15

B=1-3-4/15=5-4/15=1/15

Sacrificing ratio of S:J:B=1:1:1

Page No 5.86:

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.

Answer:

Calculation of New Ratio

Old Ratio of Kabir and Farid 7 : 3

Kabir sacrifices his share of profit in favour of Jyoti=210

Farid sacrifices his share of profit in favour of Jyoti =110

Jyoti's Share=210+110=310

New Ratio = Old Share − Share Sacrificed

Kabir's New Share=710-210=510Farid's New Share=310-110=210

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.

Page No 5.86:

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 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.

Answer:

_(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

New profit sharing ratio =

12/30

8/30

1/6

12/30

8/30

5/30

(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

New profit sharing ratio =

19/60

1/5

1/6

19/60

12/60

10/60

(vi)

	A	B
OLD RATION	3 :	2

C admits for 1/5 share of profit

Let the combined share of all partners after C’s admission be = 1

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

=1-1/4

=3/4

New ratio of A and B each= Combined share of A and B×1/2

=3/4×1/2=3/8 each

	X		Y		Z
New profit sharing ratio =	3/8	:	3/8	:	¼
=	3/8	:	3/8	:	2/8
=	3	:	3	:	2

Page No 5.87:

Question 10:

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.