Question

P, Q and R were partners in a firm sharing profits in the ratio of 3 : 2 : 1. They admitted S as a new partner for `1/8`th share in the profits, which he acquired `1/16`th from P and `1/16`th from Q. Calculate new profit-sharing ratio of P, Q, R and S.

Answer 1

P’s new Share = `3/6 - 1/16`

= `(3 xx 8)/(6 xx 8) - (1 xx 3)/(16 xx 3)`

= `24/48 - 3/48`

= `(24 - 3)/48`

= `21/48`

Q’s new Share = `2/6 - 1/16`

= `(2 xx 8)/(6 xx 8) - (1 xx 3)/(16 xx 3)`

= `16/48 - 3/48`

= `(16 - 3)/48`

= `13/48`

R’s new Share = `1/6`

= `(1 xx 8)/(6 xx 8)`

= `8/48`

S’s new Share = `1/8`

= `(1 xx 6)/(8 xx 6)`

= `6/48`

The new profit-sharing ratio for A, B, C and D = `21/48 : 13/48 : 8/48 : 6/48` or 21 : 13 : 8 : 6.