A, B and C are partners sharing profits and losses in the ratio of 5 : 4 : 1. Calculate new profit-sharing ratio, sacrificing ratio and gaining ratio in each of the following cases:
Case 1. C acquires 1/5th share from A.
Case 2. C acquires 1/5th share equally form A and B.
Case 3. A, B and C will share future profits and losses equally.
Case 4. C acquires 1/10th share of A and 1/2 share of B.
Calculation of new profit sharing ratio:
Case 1:
Partner A, B and C Old Ratio = 5:4:1
C Aquaires `1/5`th from A
A's Sacrifice Ratio = `1/5`
∴ C's Gain = `1/5`
Calculation for Partner's New Share,
A = `5/10` - `1/5` = `"5-2"/"10"` = `3/10`
B = `4/10`
C = `1/10` + `1/5` = `"1 + 2"/"10"` = `3/10`
A:B:C = 3:4:3
Case 2:
Partner A, B and C Old Ratio = 5:4:1
C Aquaires `1/5`th from A
A's Sacrifice Ratio = `1/10`
B's Sacrifice Ratio = `1/10`
∴ C's Gain = `1/5`
Calculation for Partner's New Share,
A = `5/10` - `1/10` = `"5-1"/"10"` = `4/10`
B = `4/10` - `1/10` = `"4-1"/"10"` = `3/10`
C = `1/10` + `1/5` = `"1 + 2"/"10"` = `3/10`
A:B:C = 4:3:3
Case 3:
Partner A, B and C Old Ratio = 5:4:1
Partner A, B and C New Ratio = 1:1:1
A = `5/10` - `1/3` = `"15-10"/"10"` = `5/30` [Sacrifice]
B = `4/10` - `1/3` = `"12-10"/"30"` = `2/30` [Gain]
C = `1/10` + `1/3` = `"3-10"/"30"` = `7/30` [Gain]
A:B:C = 4:3:3
Case 4:
Partner A, B and C Old Ratio = 5:4:1
C Aquaires `1/5`th from A
A's Sacrifice to Partner C = `5/10``\times``1/10` = `1/20`
B's Sacrifice to Partner C = `4/10``\times``1/2` = `4/20`
∴ C's Gain = `1/20` + `4/20` = `5/20`
Calculation for Partner's New Share,
A = `5/10` - `1/20` = `"10-1"/"20"` = `9/20`
B = `4/10` - `4/20` = `"8-4"/"10"` = `4/20`
C = `1/10` + `5/10` = `"2 + 5"/"10"` = `7/20`
A:B:C = 9:4:7
Case 1:
Partner A, B and C Old Ratio = 5:4:1
C Aquaires `1/5`th from A
A's Sacrifice Ratio = `1/5`
∴ C's Gain = `1/5`
Calculation for Partner's New Share,
A = `5/10` - `1/5` = `"5-2"/"10"` = `3/10`
B = `4/10`
C = `1/10` + `1/5` = `"1 + 2"/"10"` = `3/10`
A:B:C = 3:4:3
Case 2:
Partner A, B and C Old Ratio = 5:4:1
C Aquaires `1/5`th from A
A's Sacrifice Ratio = `1/10`
B's Sacrifice Ratio = `1/10`
∴ C's Gain = `1/5`
Calculation for Partner's New Share,
A = `5/10` - `1/10` = `"5-1"/"10"` = `4/10`
B = `4/10` - `1/10` = `"4-1"/"10"` = `3/10`
C = `1/10` + `1/5` = `"1 + 2"/"10"` = `3/10`
A:B:C = 4:3:3
Case 3:
Partner A, B and C Old Ratio = 5:4:1
Partner A, B and C New Ratio = 1:1:1
A = `5/10` - `1/3` = `"15-10"/"10"` = `5/30` [Sacrifice]
B = `4/10` - `1/3` = `"12-10"/"30"` = `2/30` [Gain]
C = `1/10` + `1/3` = `"3-10"/"30"` = `7/30` [Gain]
A:B:C = 4:3:3
Case 4:
Partner A, B and C Old Ratio = 5:4:1
C Aquaires `1/5`th from A
A's Sacrifice to Partner C = `5/10``\times``1/10` = `1/20`
B's Sacrifice to Partner C = `4/10``\times``1/2` = `4/20`
∴ C's Gain = `1/20` + `4/20` = `5/20`
Calculation for Partner's New Share,
A = `5/10` - `1/20` = `"10-1"/"20"` = `9/20`
B = `4/10` - `4/20` = `"8-4"/"10"` = `4/20`
C = `1/10` + `5/10` = `"2 + 5"/"10"` = `7/20`
A:B:C = 9:4:7
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