Question

A and B are partners sharing profits in the ratio of 3 : 2. They admit C into the partnership, giving him `1/2` share in profits, which he acquires from A and B in the ratio of 3 : 1. Calculate the new profit ratio.

Answer 1

C acquired her share of profit = `1/2` from A and B in the ratio of 3 : 1. This means

C gets `3/4 xx 1/2 = 3/8` From A

C gets `1/4 xx 1/2 = 1/8` From B

Hence,

New ratio of A = `3/5 - 3/8`

= `(3 xx 8)/(5 xx 8) - (3 xx 5)/(8 xx 5)`

= `24/40 - 15/40`

= `(24 - 15)/40`

= `9/40`

New ratio of B = `2/5 - 1/8`

= `(2 xx 8)/(5 xx 8) - (1 xx 5)/(8 xx 5)`

= `16/40 - 5/40`

= `(16 - 5)/40`

= `11/40`

New ratio of C = `1/2`

= `(1 xx 20)/(2 xx 20)`

= `20/40`

The new profit-sharing ratio of A, B and C = `9/40 : 11/40 : 20/40` or 9 : 11 : 20