Question

A, B and C were partners sharing profits in the ratio of 4 : 3 : 2. B retires from the firm. Calculate the new ratio, if

1. B's share was taken up by A and C in the ratio of 2 : 1.
2. B's share was taken up by A and C equally.
3. B's share was taken up by A only.

Answer 1

Old ratio = A : B : C = 4 : 3 : 2

B's share = `3/9 = 1/3`

(i) B's share is taken up by A and C in the ratio 2 : 1

A's gain:

`1/3 xx 2/3 = 2/9`

C's gain:

`1/3 xx 1/3 = 1/9`

New shares:

`A = 4/9 + 2/9 = 6/9`

`C = 2/9 + 1/9 = 3/9`

New Ratio = 6 : 3 = 2 : 1

(ii) B's share is taken up by A and C equally

Each gets:

`1/3 xx 1/2 = 1/6`

New shares:

`A = 4/6 + 1/6 = 11/18`

`C = 2/9 + 1/6 = 7/18`

New ration = 11 : 7

(iii) B's share is taken up by A only

A gets the entire `1/3`

`A = 4/9 + 3/9 = 1/3`

`C = 2/9`

New ratio = 7 : 2