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प्रश्न
A, B and C are partners in a firm sharing profits and losses in the ratio of 4 : 3 : 2. B decides to retire from the firm. Calculate new profit-sharing ratio of A and C in the following circumstances:
(a) If B gives his share to A and C in the original ratio of A and C.
(b) If B gives his share to A and C in equal proportion.
(c) If B gives his share to A and C in the ratio of 3 : 1.
(d) If B gives his share to A only.
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उत्तर
Old Ratio (A, B and C) = 4 : 3 : 2
B retires from the firm.
His profit share = `3/9`
Case (a) B gives his share to A and C in their original ratio.
Original Share (A and C) = 4 : 2
Share taken by A = `3/9 xx 4/6 = 12/54`
Share taken by C = `3/9 xx 2/6 = 6/54`
New Ratio = Old Ratio + Share acquired from B
A's New share = `4/9 + 12/54 = 24+12/54 = 36/54`
C's New share = `2/9 + 6/54 = 12+6/54 = 18/54`
∴ New Profit Ratio (A and C) = 36 : 18 or 2 : 1
Case (b) B gives his share to A and C in equal proportion.
Share taken by A = `3/9 xx 1/2 = 3/18`
Share taken by C = `3/9 xx 1/2 = 3/18`
New Ratio = Old Ratio + Share acquired from B
A's New share = `4/9 + 3/18 = (8+3)/18 = 11/18`
C's New Share = `2/9 + 3/18 = (4+3)/18 = 7/18`
∴ New Profit Ratio (A and C) = 11 : 7
Case (c) B gives his to A and C in the ratio 3 : 1.
Share taken by A = `3/9 xx 3/4 = 9/36`
share taken by C = `3/9 xx 1/4 = 3/36`
New Ratio = Old Ratio + Share acquired from B
A's New share = `4/9 + 9/36 = (16+9)/36 = 25/36`
C's New share = `2/9 + 3/36 = (8+3)/36 = 11/36`
∴ New Profit Ratio (A and C) = 25 : 11
Case (d) B gives his share to A only.
A’s New Share = A’s Old Share + Share of B = `4/9 + 3/9 = 7/9`
C’s Share = `2/9`
∴ New Profit Ratio (A and C) = 7 : 2
