Question 6:
Mohan and Mahesh
are partners in a firm sharing profits and losses in the ratio of 3 : 2. Nusrat is admitted
as partner with 1/4 share in profit. Nusrat
takes his share from Mohan and Mahesh in the ratio of 2 : 1. Calculate new profit-sharing ratio.
Answer:
Old
Profit Sharing Ratio amongst Partners (Mohan and Mahesh) is 3
: 2
Nusrat is admitted for 1/4th
Share in Profits
Sacrificing Ratio of Mohan and Mahesh is 2 : 1
Nusrat acquires =2/3×1/4=2/12 from Mohan
Nusrat acquires =1/3×1/4=1/12 from Mahesh
New ratio= old ratio – new ratio
Mohan‘s new share=3/5
-2/12 =36-10/60=26/60
Mahesh ‘s new share=2/5 -1/12
=24-5/60=19/60
Nusrat’s share=1/4=15/60
New
ratio= 26:19:15
Question 7: S, B and J were partners in a firm. T was admitted as a partner in the partnership firm for 1/5th share of profits. Calculate the sacrificing ratio of S, B and J. (CBSE 2019)
Answer:
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
S=4/5×1/3=4/15
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
Question 8: P and Q were partners in a
firm sharing profits in the ratio of 5:3. R was admitted for 1/4th share in the
profits, of which he took 75% from P and the remaining from Q. Calculate the sacrificing
ratio of P and Q. (CBSE 2020)
Answer:
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
Question 9:
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=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.
Question 10:
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.
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 1/4th 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 3/10th
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