Question

Calculate new ratios and sacrificing ratios in the following cases:

1. A, B and C are partners sharing profits in the ratio of 4 : 3 : 2. D is admitted for `1/3`rd share.
2.  A, B and C are partners sharing profits in the ratio of `1/2`, `1/3` and `1/6`. D is admitted for a `1/6`th share of profits.
3. A, B and C are partners sharing profits in the ratio of `6/14`, `5/14`, and `3/14`. D is admitted for `1/8`th share of profits.

Answer 1

i. Calculation of New Ratio:

The total share is 1. D is admitted for a `1/3` share.

Remaining share for A, B, and C = `1 - 1/3`

= `2/3`

A’s new share = `4/9 xx 2/3`

= `8/27`

B’s new share = `3/9 xx 2/3`

= `6/27`

C’s new share = `2/9 xx 2/3`

= `4/27`

D’s share = `1/3`

= `(1 xx 9)/(3 xx 9)`

= `9/27`

The new profit-sharing ratio = `8/27 : 6/27 : 4/27 : 9/27` or 8 : 6 : 4 : 9

Calculation of Sacrificing Ratio:

A’s sacrifice = `4/9 - 8/27`

= `(4 xx 3)/(9 xx 3) - 8/27`

= `12/27 - 8/27`

= `(12 - 8)/27`

= `4/27`

B’s sacrifice = `3/9 - 6/27`

= `(3 xx 3)/(9 xx 3) - 6/27`

= `9/27 - 6/27`

= `(9 - 6)/27`

= `3/27`

C’s sacrifice = `2/9 - 4/27`

= `(2 xx 3)/(9 xx 3) - 4/27`

= `6/27 - 4/27`

= `(6 - 4)/27`

= `2/27`

The sacrificing ratio of A, B, and C = `4/27 : 3/27 : 2/27` or 4 : 3 : 2

ii. Calculation of New Ratio:

The total share is 1. D is admitted for `1/6` share.

Remaining share for A, B, and C = `1 - 1/6`

= `5/6`

A’s new share = `3/6 xx 5/6`

= `15/36`

B’s new share = `2/6 xx 5/6`

= `10/36`

C’s new share = `1/6 xx 5/6`

= `5/36`

D’s share = `1/6`

= `(1 xx 6)/(6 xx 6)`

= `6/36`

The new profit-sharing ratio = `15/36 : 10/36 : 5/36 : 6/36` or 15 : 10 : 5 : 6

Calculation of Sacrificing Ratio:

A’s sacrifice = `3/6 - 15/36`

= `(3 xx 6)/(6 xx 6) - 15/36`

= `18/36 - 15/36`

= `(18 - 15)/36`

= `3/36`

B’s sacrifice = `2/6 - 10/36`

= `(2 xx 6)/(6 xx 6) - 10/36`

= `12/36 - 10/36`

= `(12 - 10)/36`

= `2/36`

C’s sacrifice = `1/6 - 5/36`

= `(1 xx 6)/(6 xx 6) - 5/36`

= `6/36 - 5/36`

= `(6 - 5)/36`

= `1/36`

The sacrificing ratio of A, B, and C = `3/36 : 2/36 : 1/36` or 3 : 2 : 1

iii. Calculation of New Ratio:

The total share is 1. D is admitted for `1/8` share.

Remaining share for A, B, and C = `1 - 1/8`

= `7/8`

A’s new share = `6/14 xx 7/8`

= `42/112`

B’s new share = `5/14 xx 7/8`

= `35/112`

C’s new share = `3/14 xx 7/8`

= `21/112`

D’s share = `1/8`

= `(1 xx 14)/(8 xx 14)`

= `14/112`

The new profit-sharing ratio = `42/112 : 35/112 : 21/112 : 14/112`or 42 : 35 : 21 : 14

Calculation of Sacrificing Ratio:

A’s sacrifice = `6/14 - 42/112`

= `(6 xx 8)/(14 xx 8) - 42/112`

= `48/112 - 42/112`

= `(48 - 42)/112`

= `6/112`

B’s sacrifice = `5/14 - 35/112`

= `(5 xx 8)/(14 xx 8) - 35/112`

= `40/112 - 35/112`

= `(40 - 35)/112`

= `5/112`

C’s sacrifice = `3/14 - 21/112`

= `(3 xx 8)/(14 xx 8) - 21/112`

= `24/112 - 21/112`

= `(24 - 21)/112`

= `3/112`

The sacrificing ratio of A, B, and C = `6/112 : 5/112 : 3/112` or 6 : 5 : 3