PARTNERSHIP ACCOUNTS - New profit sharing ratio & sacrificing ratio

1. Ms. K. KALAI SELVI
Assistant Professor of Commerce
PG & Research Department of Commerce
Bon Secours College for Women, Thanjavur

2. New Profit Sharing Ratio
Sum No.1
(Answer for Sum No.1)
A : B
7 : 3
C – 2/7th
Share
Profit = 1
Remaining share of profit = 1 – 2/7
= 5/7
Remaining share of profit shared by the old partners in their old ratio (7:3)
A = 5/7 x 7/10 = 35/70
B = 5/7 x 3/10 = 15/70
C's share = 2/7 multiply by 10 = 20/70
A : B : C
35 : 15 : 20
7 : 3 : 4
Sum No.2
(Answer for Sum No.2)
A : B
7 : 3
C – 3/7th
Share
Profit = 1
Remaining share of profit = 1 – 3/7
= 4/7
Remaining share of profit shared by the old partners in their old ratio (7:3)
A = 4/7 x 7/10 = 28/70
B = 4/7 x 3/10 = 12/70
C's share = 3/7 multiply by 10 = 30/70
A : B : C
28 : 12 : 30
14 : 6 : 15

3. Sum No.3
(Answer for Sum No.3)
A = 1 / 6
B = 1 / 3
C – 1/2nd
Share
Profit = 1
Remaining share of profit = 1 – 1/2
= 1/2
Remaining share of profit shared by the old partners
The denominators are not same. Hence we took LCM
A : B
= 1 : 2 divided by 6
A = 1/2 x 1/3 = 1/6
B = 1/2 x 2/3 = 2/6
C's share = 1/2 multiply by 3 = 3/6
A : B : C
1 : 2 : 3
Sum No.4
(Answer for Sum No.4)
Thangam : Nathan
5 : 3
Saravanan joins = 3 / 8 th share
Remaining share of profit = 5 / 8
T = 5/8 x 5/8 = 25/64
N = 5/8 x 3/8 = 15/64

4. S = 3 / 8 multiply by 8 = 24/64
T : N : S
25 : 15 : 24
Sum No.5
(Answer for Sum No.5)
X : Y
7 : 5
Z = 1 / 6 th share in profits
From X - 1/24th
From Y – 1/8th
X = 7 / 12 - 1/24
Take LCM for 12 & 24
= 14 – 1 /24 = 13/24
Y = 5 / 12 - 1/8
Take LCM for 12 & 8
= 10 – 3 /24 = 7/24
Z = 1/ 24 + 1/8 = 1+3 / 24 = 4 / 24
X : Y : Z
13 : 7 : 4
Sum No.6
(Answer for Sum No.6)
Karthik : Sarathy
3 : 2

5. Doss = 1/3
(a) Equally from old partners
1/3 diveded by 2
1/3 x ½ = 1/6
K = 3/5 – 1/6 = 13/30
S = 2/5 – 1/6 = 7 /30
D = 1/3 Multiply by 10 = 10/30
K : S : D
13 : 7 : 10
(b) If Doss acquired as 3/12th
from Karthik and 1/12th
from Sarathy
K = 3 / 5 – 3 / 12 = 36 – 15/60 = 21 /60
S = 2/ 5 – 1 / 12 = 24 – 5 /60 = 19 /60
D = 3/12 + 1/12 = 4 /12 Multiply by 5 = 20 / 60
K : S : D
21 : 19 : 20
Sum No. 7
(Answer for Sum No.7)
A : B
5 : 2
C = 2 /5
Remaining = 3 /5
A = 5 / 7 X 3 / 5 =15 / 35

6. B = 2 / 7 X 3/5 = 6 / 35
C = 2/5 Multiply by 7 = 14 /35
A : B : C
15 : 6 : 14
Sum No. 8
(Answer for Sum No.8)
Prem : Chandra
7 : 3
1/7th
from Prem
Rama
1/3rd
from Chandra
The total number of share will not be changed. It remains in 10
Prem’s New Ratio = 7 – 1 = 6
Chandra New Ratio = 3 – 1 = 2
Rama’s Share = 1 + 1 = 2
Prem : Chandra : Rama
6 : 2 : 2
3 : 1 : 1
Sum No. 9
(Answer for Sum No.9)
X : Y
3 : 2

7. Z – 1 / 5 th share; he gets entire share from X
The total share also = 5
( 3 + 2 = 5 )
Hence
X ‘s new share will be = 3 – 1 = 2
Y’s share (will be remains the same) = 2
Z’s share is = 1
X : Y : Z
2 : 1 : 1
Sum No. 10
(Answer for Sum No.10)
A : B
5 : 3
C – 1/ 4 th share
Remaining share = 3 / 4
A = 3 / 4 x 5 / 8 = 15 / 32
B = 3 / 4 x 3 / 8 = 9 / 32
C = 1 /4 Multiply by 8 both side = 8 / 32
A : B : C
15 : 9 : 8
Sum No. 11
(Answer for Sum No.11)
A : B
5 : 3

8. C – 1 /4 th share equally from A and B
1 / 4 Divided by 2
Hence
1 / 4 x 1 / 2 = 1 / 8
There fore
A’s New Share will be = 5 / 8 – 1 / 8 = 4 / 8
B’s New Share will be = 3 / 8 – 1 / 8 = 2 / 8
C’s Share = 1 / 4 Multiply by 2 = 2 / 8
A : B : C
4 : 2 : 2
2 : 1 : 1
Sum No. 12
(Answer for Sum No.12)
A : B
2 : 3
4 / 20 from A
C – 1 / 4
1 / 20 from B
8 - 4
A = 2 / 5 – 4 / 20 = = 4 / 20
20
12 - 1
B = 3 / 5 – 1 / 20 = = 11 / 20
20
C = 1 / 4 Multiply by 5 = 5 / 20
A : B : C
4 : 11 : 5

9. Sum No. 13
(Answer for Sum No.13)
A : B
1 : 1
C – acquires 1 / 4 th from A
- acquires 1 / 3 rd from B
A’s New share will be = 1 – 1 /4 = 3 / 4
B’s New share will be = 1 – 1 /3 = 2 / 3
C’s Share = 1 /4 + 1 / 3 = 3 + 4 / 12 = 7 / 12
A : B : C
¾ : 2/3 : 7/12
LCM
= 9 ; 8 ; 7 / 12
A : B : C
9 : 8 : 7
Sacrificing Ratio
Sum No. 14
(Answer for Sum No.14)
P : Q
4 : 3
R is admitted in the business
New Ratio
P : Q : R
2 : 2 : 3
Sacrificing Ratio = Old Ratio – New Ratio
P = 4 /7 – 2 / 7 = 2 / 7
Q = 3 / 7 – 2 / 7 = 1 / 7

10. Sacrificing Ratio
P : Q
2 : 1
Sum No. 15
(Answer for Sum No.15)
A : B
3 : 1
C – 1 / 8 th share
Remaining share = 7 / 8
A’s New share = 3 / 4 x 7 / 8 =21 / 32
B’s New share = 1 / 4 x 7 / 8 = 7 / 32
C’s share = 1 / 8 Multiply by 4 = 4 / 32
New Ratio
A : B : C
21 : 7 : 4
Sacrificing Ratio = Old Ratio – New Ratio
A = 3 / 4 – 21 / 32 = 24 – 21 / 32 = 3 / 32
B = 1 / 4 – 7 / 32 = 8 – 7 / 32 = 1 / 32
Sacrificing Ratio
A : B
3 : 1
Sum No. 16
(Answer for Sum No.16)
A : B : C
4 : 3 : 2
D – 1 /3

11. Remaining Profit = 2 /3
A’s New share = 4 / 9 x 2 / 3 = 8 / 27
B’s New share = 3 / 9 x 2 / 3 = 6 / 27
C’s New share = 2 / 9 x 2 / 3 = 4 / 27
D’s share = 1 / 3 Multiply by 9 = 9 / 27
New Ratio
A : B : C : D
8 : 6 : 4 : 9
Sacrificing Ratio = Old Ratio – New Ratio
A = 4 / 9 – 8 / 27 = 12 - 8 / 27 = 4 / 27
B = 3 / 9 – 6 / 27 = 9 - 6 / 27 = 3 / 27
C = 2 / 9 – 4 / 27 = 6 - 4 / 27 = 2 / 27
Sacrificing Ratio
A : B : C
4 : 3 : 2
Sum No. 17
(Answer for Sum No.17)
A : B
5 : 3
C – 1 / 6
Remaining Profit = 5 / 6
A’s New share = 5 / 6 x 5 / 8 = 25 / 48
B’s New share = 5 / 6 x 3 / 8 = 15 / 48
C’s share = 1 / 6 Multiply by 8 = 8 / 48
New Ratio
A : B : C
25 : 15 : 8
Sacrificing Ratio = Old Ratio – New Ratio
A = 5 / 8 – 25 / 48 = 30 - 25 / 48 = 5 / 48
B = 3 / 8 – 15 / 48 = 18 - 15 / 48 = 3 / 48

12. Sacrificing Ratio
A : B
5 : 3
Sum No. 18
(Answer for Sum No.18)
M : N
5 : 3
C – gets 4 /20 th share from M
- gets 2 / 20 th share from N
M’s New share = 5 / 8 – 4 / 20 = 25 – 8 / 40 = 17 / 40
N’s New share = 3 / 8 – 2 / 20 = 15 – 4 / 40 = 11 / 40
C’s share = 4 / 20 + 2 / 20 = 6 / 20 Multiply by 2 = 12 / 40
New Ratio
M : N : C
17 : 11 : 12
Sacrificing Ratio = Old Ratio – New Ratio
M = 5 / 8 – 17 / 40 = 25 – 17 / 40 = 8 / 40
N = 3 / 8 – 11 / 40 = 15 – 11 / 40 = 4 / 40
Sacrificing Ratio
M : N
8 : 4
2 : 1
Sum No. 19
(Answer for Sum No.19)
P : Q : R
3 : 2 : 1
S is admitted

13. New Ratio
P : Q : R : S
5 : 3 : 2 : 2
Sacrificing Ratio = Old Ratio – New Ratio
P = 3 / 6 – 5 / 12 = 6 – 5 / 12 = 1 / 12
Q = 2 / 6 – 3 / 12 = 4 – 3 / 12 = 1 / 12
R = 1 / 6 – 2 / 12 = 2 – 2 / 12 = 0 / 12
Sacrificing Ratio
P : Q
1 : 1
Sum No. 20
A, B and C are partners in proportion of 2/5, 2/5 and 1/5 respectively. D was
admitted in the firm as a partner with 1/6th
share. Calculate sacrificing ratio of
the partners.
(Answer for Sum No.20)
A : B : C
2 : 2 : 1
D is admitted – 1/ 6 th share
Remaining Share = 5 / 6
A’s New share = 5 /6 x 2 / 5 = 10 / 30
B’s New share = 5 /6 x 2 / 5 = 10 / 30
C’s New share = 5 /6 x 1 / 5 = 5 / 30
D’s share = 1 / 6 Multiply by 5 = 5 / 30
New Ratio
A : B : C : D
10 : 10 : 5 : 5
Sacrificing Ratio = Old Ratio – New Ratio
A= 2 /5 - 10 / 30 = 12 – 10 / 30 = 2 /30
B = 2 /5 - 10 / 30 = 12 – 10 / 30 = 2 /30
C = 1 / 5 - 5 / 30 = 6 – 5 / 30 = 1 /30
Sacrificing Ratio
A : B : C
2 : 2 : 1