Question

A and B are partners sharing profits in the ratio of 5 : 3. C is admitted to the partnership for `1/4`th share of future profits. Calculate the new profit sharing ratio and the sacrificing ratio.

Answer 1

Calculation of New Profit Sharing Ratios:

Let total profit be = 1.

Share given to C = `1/4`

Remaining Share = `1 - 1/4`

= `3/4`

Now the old partners will share this remaining profit in their old profit sharing ratios:

Hence,

A’s Share = `3/4 xx 5/8`

= `15/32`

B’s Share = `3/4 xx 3/8`

= `9/32`

C’s Share = `1/4`

= `(1 xx 8)/(4 xx 8)`

= `8/32`

The new profit-sharing ratio for A, B, and C is `15/32 : 9/32 : 8/32` or 15 : 9 : 8.

Calculation of Sacrificing Ratios:

Sacrifice Ratio = Old Ratio − New Ratio

A = `5/8 - 15/32`

= `(5 xx 4)/(8 xx 4) - 15/32`

= `20/32 - 15/32`

= `(20 - 15)/32`

= `5/32`

B = `3/8 - 9/32`

= `(3 xx 4)/(8 xx 4) - 9/32`

= `12/32 - 9/32`

= `(12 - 9)/32`

= `3/32`

B = `1/4 - 8/32`

= `(1 xx 8)/(4 xx 8) - 8/32`

= `8/32 - 8/32`

= `(8 - 8)/32`

= 0

Sacrificing ratio = 5 : 3