Question

P, Q, R and S were partners in a firm sharing profits and losses in the ratio of 4 : 3 : 2 : 1. On 31st March, 2022, P retired from the firm. P's share was taken over by Q, R and S in the ratio of 1 : 2 : 3. Calculate the new profit sharing ratio of Q, R, and S.

Answer 1

Old ratio = P : Q : R : S = 4 : 3 : 2 : 1

P's share = `4/10 = 2/5`

P's share is acquired by Q, R and S in the ratio 1 : 2 : 3.

Their respective gains:

Q = `2/5 xx 1/6 = 1/15` 

R = `2/5 xx 2/6 = 2/15`

S = `2/5 xx 3/6 = 1/5`

New shares:

Q = `3/10 + 1/15 = 11/30` 

R = `2/10 + 2/15 = 10/30` 

S = `1/10 + 1/5 = 9/30` 

Therefore, the new profit-sharing ratio = 11 : 10 : 9.