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.
A and B are partners. They admit C for 1/4th share. In future, the ratio between A and B would be 2: 1.
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.
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.
A and B are equal partners. They admit C and D as partners with 1/5th and 1/6th share respectively.
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.
The solution of Question 09Chapter 5 of +2-A
Case I
Old Ratio of R and T
=
3: 2
R Sacrifice his share in the favour of S
=
1/4^{th}
T Sacrifice his share in the favour of S
=
1/5^{th}
In this case, we have to calculate the sacrificing share of both partners with the following formula and then subtract this share from the profit share of old partners: –
Sacrificing Share of Old Partners = New Partner’s Share X Sacrificed Ratio
R Sacrificing Share
=
3
X
1
5
4
=
3
20
T Sacrificing Share
=
2
–
1
5
5
=
2
25
New Ratio of Old Partners = Old Ratio – Sacrificed Ratio
R New Profit Share
=
3
+
3
5
20
=
12 – 3
20
=
9
20
T New Profit Share
=
2
+
2
5
25
=
10 – 2
25
=
8
25
S’s Share = R’s Sacrificing + T’s Sacrificing
T New Profit Share
=
3
+
2
20
25
=
15 + 8
100
=
23
100
New Profit sharing Ratio between All partners
=
9
:
8
:
23
20
25
100
=
45: 32: 23
100
=
45: 32: 23
Case II
Old Ratio of A and B
=
2: 1
C is admitted for 1/4th share of profit
Let the total share of the business = 1 The remaining share of A and B after C’s Admission = Total Share – C’s Share
T New Profit Share
=
1
–
1
4
=
4 – 1
4
=
3
4
To Calculate to New Ratio distribute the remaining share in the old ratio of old partners’
New Ratio = Combined share of A and B X Old Ratio
A’s New Ratio
=
3
+
2
4
3
=
6
12
B’s New Ratio
=
3
+
1
4
3
=
3
12
C’s New Ratio
=
1
+
3
4
3
=
3
12
New Profit sharing Ratio between A, B and C
=
6 : 3 : 3
=
2: 1: 1
Case III
Old Ratio of A and B
=
3: 2
C admits for 1/5th share of profit
C acquires 1/5th of his share from A
C acquires 4/5th of his share from B
Sacrificing Share of Old Partners = C’s Share x Sacrificed Ratio
A’s Sacrifice Share
=
1
x
1
5
5
=
1
25
B’s Sacrifice Share
=
1
X
4
5
25
=
4
25
New Ratio of Old Partners = Old Ratio – Sacrificed Ratio
A’s Sacrifice Share
=
3
–
1
5
25
=
15 – 1
100
=
14
25
B New Profit Share
=
2
–
4
5
25
=
10 – 4
25
=
6
25
C’s Share
=
1
x
5
5
5
=
5
25
New Profit sharing Ratio between All partners
=
14: 6: 5
Case IV
Old Ratio of X, Y and Z
=
3: 2: 1
W is admitted for 1/6th share of profit
Z would retain his original share. So we have to subtract z share also from total
Let the total share of the business = 1 The remaining share of X and Y = Total Share – W’s Share – Z’s Share
Remaining share
=
1
–
1
–
1
6
6
=
6 – 1 – 1
6
=
4
6
To Calculate to New Ratio distribute the remaining share in the old ratio of old partners’ New Ratio = Remaining share for X and Z X Old Ratio
X’s New Ratio
=
4
x
3
6
5
=
12
30
Y’s New Ratio
=
4
x
2
6
5
=
12
30
Z’s New Ratio
=
1
x
5
6
5
=
5
30
W’s New Ratio
=
1
x
5
6
5
=
5
30
New Profit sharing Ratio between All partners
=
12: 8: 5: 5
Case V
Old Ratio of A and B
=
1: 1
C is admitted for 1/5th share of profit
D is admitted for 1/6th share of profit
Let the total share of the business = 1 The remaining share of A and B = Total Share – C’s Share – D’s Share
Remaining share
=
1
–
1
–
1
5
6
=
30 – 6 -5
30
=
19
30
To Calculate to New Ratio distribute the remaining share in the old ratio of old partners’
New Ratio = Remaining share for A and B X Old Ratio
A’s New Ratio
=
19
x
1
30
2
=
19
60
B’s New Ratio
=
19
x
1
30
2
=
19
60
C’s New Ratio
=
1
x
12
5
12
=
12
60
D’s New Ratio
=
1
x
10
6
10
=
10
60
New Profit sharing Ratio between All partners
=
19: 19: 12: 10
Case VI
Old Ratio of A and B
=
3: 2
C is admitted for 1/4th share of profit
Let the total share of the business = 1 The remaining share of A and B after C’s Admission = Total Share – C’s Share
Remaining share
=
1
–
1
4
=
4 – 1
4
=
3
4
To Calculate to New Ratio distribute the remaining share in the Equal ratio of old partners’ because they decide to share future profit equal.