Question

Find New Profit-sharing Ratio:
(i) R and T are partners in a firm sharing profits in the ratio of 3 : 2. S joins the firm. R surrenders 1/4th of his share and T 1/5th of his share in favour of S.
(ii) A and B are partners. They admit C for 1/4th share. In future, the ratio between A and B would be 2 : 1.
(iii) A and B are partners sharing profits and losses in the ratio of 3 : 2. They admit C for 1/5th share in the profit. C acquires 1/5th of his share from A and 4/5th share from B.
(iv) X, Y and Z are partners in the ratio of 3 : 2 : 1. W joins the firm as a new partner for 1/6th share in profits. Z would retain his original share.
(v) A and B are equal partners. They admit C and D as partners with 1/5th and 1/6th share respectively.
(vi) A and B are partners sharing profits/losses in the ratio of 3 : 2 . C is admitted for 1/4th share. A and B decide to share equally in future.

Answer 1

_(i)

S’s Share = R’s Sacrifice + S’s Sacrifice

(ii)

C admits for 1/4^th share of profit

Let the combined share of A, B and C be = 1

Combined share of A and B

New Ratio = Combined share of A and B

(iii)

C admits for share of profit

New Ratio = Old Ratio − Sacrificing Ratio

(iv)

W admits for share of profit

Let combined share of all partner after W’s admission be = 1

Combined share X and Y in the new firm

New Ratio = Old Ratio × Combined share of X and Y

(v)

C admits for share

D admits for share

Let combined share of all partner after C and D’s admission be = 1

Combined share of profit of A and B after C and D’s admission

New Ratio = Old Ratio × Combined share of A and B

(vi)

C admits for share of profit

Let the combined share of all partners after C’s admission be = 1

Combined share of A and B after C’s admission