Question

A and B share profits in the ratio of 3 : 2. They agreed to admit C on the condition that A will sacrifice 3/20th of his share of profit in favour of C and B will sacrifice 1/20th of his profits in favour of C. Calculate new profit sharing ratio.

Answer 1

1. Individual Sacrifice by A and B

Old Ratio of A and B: 3 : 2

A's Old Share: `3/5`

B's Old Share: `2/5`

A's Sacrifice (`3/20` of his share)

`3/5 xx 3/20 = 9/100`

B's Sacrifice (`1/20` of his share)

`2/5 xx 1/20 = 2/100`

2. Calculation of New Shares

Formula: New Share = Old Share − Sacrificed Share

A's New Share:

`3/5 - 9/100 = (60 - 9)/100 = 51/100`

B's New Share:

`2/5 - 2/100 = (40 - 2)/100 = 38/100`

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

`9/100 + 2/100 = 11/100`

Since all fractions already have a common denominator of 100, the New Profit Sharing Ratio among A, B, and C is:

51 : 38 : 11