Question

A and B are partners sharing profits in the ratio of 3 : 2. C is admitted for 1/5th share of profits out of which half share was gifted by A and the remaining share was taken by C equally from A and B. Calculate new profit sharing ratio.

Answer 1

1. Individual Sacrifice by A and B

Total Share of C: `1/5`

Half Share gifted by A:

`1/5 xx 1/2 = 1/10`

Remaining Share of C:

`1/5 - 1/10 = 1/10`

Remaining Share taken equally from A and B:

From A: `1/10 xx 1/2 = 1/20`

From B: `1/10 xx 1/2 = 1/20`

2. Total Sacrifice

Total Sacrifice by A: `1/10 "(gift)" + 1/20 = (2 + 1)/20 = 3/20`

Total Sacrifice by B: `1/20`

3. Calculation of New Shares

Formula: New Share = Old Share − Total Sacrifice

A's New Share: `3/5 - 3/20 = (12 - 3)/20 = 9/20`

B's New Share: `2/5 - 1/20 = (8 - 1)/20 = 7/20`

C's New Share: `1/5 = (1 xx 4)/(5 xx 4) = 4/20`

The New Profit Sharing Ratio among A, B, and C is:

9 : 7 : 4