Question

P, Q and R are in partnership sharing profits and losses as 1/2, 2/6 and 1/6 respectively. R retires and his share is taken by P and Q in the ratio of 2 : 1. Immediately, Sis admitted for 1/4th share of profit, 1/3rd of which was given by P and the remaining share was taken equally from P and Q. Calculate new profit-sharing ratio after S's admission.

Answer 1

R = 1/6

P gains from R = `2/3xx1/6=2/18=1/9`

Q gains from R = `1/3xx1/6=1/18`

P's new share after R's retirement = `1/2+1/9=(9+2)/18=11/18`

Q's new share after R's retirement = `2/6+1/18=6+1/18=7/18`

S's share is `1/4`

P's sacrifice for S = `1/3xx1/4=1/12`

Remaining share for S = `1/4-1/12=(3-1)/12=2/12=1/6`

P's additional sacrifice for S = `1/2xx1/6=1/12`

Q's sacrifice for S = `1/2xx1/6=1/12`

P's new share = `11/18-1/12-1/12=16/36`

Q's new share = `7/18-1/12=(14-3)/36=11/36`

S's new share = `1/4=9/36`

The new ratio is P : Q : S = `16/36:11/36:9/36`

The new profit-sharing ratio is 16 ∶ 11 ∶ 9