Question

A, B and C are partners in a firm sharing profits in the ratio of 5 : 3 : 2. A retires and his share is taken up by B and C equally. Find the new profit sharing ratio and the gaining ratio.

Answer 1

1. Calculation of Gaining Ratio

Since A's share of `5/10` is taken up by B and C equally, their gaining ratio is explicitly given as equal.

Gaining Ratio of B and C = 1 : 1

2. Calculation of New Profit Sharing Ratio

Old Shares:

`A = 5/10`

`B = 3/10`

`C = 2/10`

Share acquired from A:

B acquires = `5/10 xx 1/2 = 5/20`

C acquires = `5/10 xx 1/2 = 5/20`

New Shares (Old Share + Share Acquired):

B's New Share = `3/10 + 5/20 = (6 + 5)/20 = 11/20`

C's New Share = `2/10 + 5/20 = (4 + 5)/20 = 9/20`

New Profit Sharing Ratio of B and C = 11 : 9