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Question

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 given his share to A and C in the original ratio of A and C.
(c) If B gives his share to A and C in equal proportion.
(d) 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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Solution

Old ratio (A, B and C) = 4: 3 :2
B retires from the firm.
His profit share = 3/9

(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 X 4/6 = 12/54
Share taken by C = 3/9 X 2/6 = 6/54

New ratio = Old ratio + Share acquired from B
A's new share = 4/9 + 12/54 = 24/54 + 12/54 = 36/54
C's new share = 2/9 + 6/54 = 12/54 + 6/54 = 18/54
Therefore, new profit ratio (A and C) = 36: 18 or 2:1

(b) B gives his share to A and C in equal proportion.

Share taken by A = 3/9 X 1/2 = 3/18

Share taken by C = 3/9 X 1/2 = 3/18

New ratio = Old ratio + Share acquired from B
A's new share = 4/9 + 3/18 = 8/18 + 3/18 = 11/18
C's new share = 2/9 + 3/18 = 4/18 + 3/18 = 7/18
Therefore, new profit ratio (A and C) = 11 : 7

(c) B gives his share to A and C in the ratio of 3 : 1

Share taken by A = 3/9 X 3/4 = 9/36
Share taken by C = 3/9 X 1/4 = 3/36

New ratio = Old ratio + Share acquired from B
A's new share = 4/9 + 9/36 =16/36 + 9/36 = 25/36
C's new share = 2/9 + 3/36 = 8/36 + 3/36 = 11/36

Therefore, new profit ratio (A and C)= 25: 11

(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 new share = 2/9
Therefore, new profit share = (A and C) = 7: 2





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