## 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.

Solution

(i)

Sacrificing Ratio = Old Ratio × Surrender Ratio
R’s = 3/5 × 1/4 = 3/20
T’s = 2/5 × 1/5 = 2/25

New Ratio = Old Ratio − Sacrificing Ratio
R = 3/5-3/20 = 9/20
T = 2/5-2/25 = 8/25
S’s Share = R’s Sacrifice + S’s Sacrifice
= 3/20 + 2/25 = 23/100

(ii)

C admits for 1/4th share of profit
Let the combined share of A, B and C be = 1
Combined share of A and B = 1-C’s share = 1-1/4 = 3/4

New Ratio = Combined share of A and B ×2/3
A’s = 3/4 × 2/3 = 6/12
B’s = 3/4 × 1/3 = 3/12

(iii)

C admits for 1/5share of profit

New Ratio = Old Ratio − Sacrificing Ratio
A’s = 3/5-1/25 = 14/25
B’s = 2/5-4/25 = 6/25

(iv)

W admits for 1/6 share of profit
Let combined share of all partner after W’s admission be = 1
Combined share X and Y in the new firm = 1- Z’s share- W’s share
= 1-1/6-1/6 = 4/6

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

(v)

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 = 1- C’s share – Z’s share
= 1-1/5-1/6 = 19/30

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

(vi)

C admits for 1/5 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 = 1 – C’s share
= 1-1/4 = 3/4

New ratio of A and B each= Combined share of A and B × 1/2
= 3/4 × 1/2 = 3/8 each