Question

A and B are partners in a firm sharing profits in the ratio of 2 : 1. С joins the firm. A surrenders 1/4th of his share and B 1/5th of his share in favour of C. Find the new profit sharing ratio.

Answer 1

Individual Sacrifice by A and B

Old Ratio of A and B: 2 : 1

A's Old Share: `2/3`

B's Old Share: `1/3`

A's Sacrifice (`1/4` of his share)

`2/3 xx 1/4 = 2/12 or 1/6`

A's Sacrifice (`1/5` of his share)

`1/3 xx 1/5 = 1/15`

2. Calculation of New Shares

Formula: New Share = Old Share − Sacrificed Share

A's New Share:

`2/3 - 1/6 = (4 - 1)/6 = 3/6 = 1/2`

B's New Share:

`1/3 - 1/15 = (5 - 1)/15 = 4/15`

C's New Share (Total share received from A and B):

`1/6 + 1/15 = (5 + 2)/30 = 7/30`

To find the final ratio, convert all fractions to have a common denominator of 30:

A: `1/2 = (1 xx 15)/(2 xx 15) = 15/30`

B: `4/15 = (4 xx 2)/(15 xx 2) = 8/30`

C: `7/30`

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

15 : 8 : 7