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

New-Profit sharing ratio is calculated below.

Explanation:

1.

Old ratio = 3:2

Sacrificing Ratio = Old Ratio $\times$ Surrender Ratio

Sacrificing ratio for R

$=\frac{3}{5} \times \frac{1}{4}=\frac{3}{20}$

Sacrificing ratio for T

$=\frac{2}{5} \times \frac{1}{5}=\frac{2}{25}$

New Ratio = Old ratio – Sacrificing ratio  

R’s share

$=\frac{3}{5}-\frac{3}{20}=\frac{12-3}{20}=\frac{9}{20}$

T’s share

$=\frac{2}{5}-\frac{2}{25}=\frac{10-2}{25}=\frac{8}{25}$

S's share = R's sacrifice + S's sacrifice

S's share will be sacrifice done by R’s and T’s

$=\frac{3}{20}+\frac{2}{25}=\frac{15+8}{100}=\frac{23}{100}$

New Profit Sharing Ratio R, T and S

$=\frac{9}{20}: \frac{8}{25}: \frac{23}{100}$

$=\frac{45: 32: 23}{100}$

New ratio can be written as 45: 32: 23

2.

Old Ratio of A and B = 1:1  

C = ¼ of the profit

Combined share of A and B will be 1- ¼ = ¾

$New Ratio = Combined share of \mathrm{A} and \mathrm{B} \times \frac{2}{3}$

New ratio will be in ratio of 2 : 1 for A and B.

A’s share

$=\frac{3}{4} \times \frac{2}{3}=\frac{6}{12}$

B’s share

$=\frac{3}{4} \times \frac{1}{3}=\frac{3}{12}$

New Profit Sharing Ratio A, B and C

$\begin{aligned}&=\frac{6}{12}: \frac{3}{12}: \frac{1}{4}\\&=\frac{6: 3: 3}{12}\\&=2: 1: 1\end{aligned}$

Thus, new ratio becomes 2 : 1 : 1

3.

Old ratio of A and B = 3:2

C’s share = 1/5 of profit

$\text { A's sacrifice }=\mathrm{C}^{\prime} \text { s share } \times \frac{1}{5}$

$=\frac{1}{5} \times \frac{1}{5}=\frac{1}{25}$

$\text { B's sacrifice }=C^{\prime} s \text { share } \times \frac{4}{5}$

$=\frac{1}{5} \times \frac{4}{5}=\frac{4}{25}$

New Ratio will be calculated when we deduct sacrificing ratio from old ratio

A’s share

$=\frac{3}{5}-\frac{1}{25}=\frac{15-1}{25}=\frac{14}{25}$

B’s share

$=\frac{2}{5}-\frac{4}{25}=\frac{10-4}{25}=\frac{6}{25}$

Thus, new ratio would be calculated as:

$\begin{aligned}&=\frac{14}{25}: \frac{6}{25}: \frac{1}{5}\\&=\frac{14: 6: 5}{25}\\&=14: 6: 5\end{aligned}$

Thus, the new ratio becomes 14 : 6 : 5

4.

Old ratio of X, Y, Z = 3:2:1

W would get 1/6th 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

$\begin{aligned}&=1-\frac{1}{6}-\frac{1}{6}=\frac{6-1-1}{6}\\&=\frac{4}{6}\end{aligned}$

New Ratio = Old Ratio $\times$ Combined share  of X and Y

X’s share

$=\frac{3}{5} \times \frac{4}{6}=\frac{12}{30}$

Y’s share

$=\frac{2}{5} \times \frac{4}{6}=\frac{8}{30}$

New profit-sharing ratio would be

$=\frac{12}{30}: \frac{8}{30}: \frac{1}{6}: \frac{1}{6}$

$\begin{aligned}&=\frac{12: 8: 5: 5}{30}\\&=12: 8: 5: 5\end{aligned}$

Thus, the  New profit-sharing ratio becomes 12 : 8 : 5 : 5

5.

Old Ratio A and B = 1:1

C would get 1/5 share and D would get 1/6 share  

Combined share of A and B after C and D gets in

$\begin{aligned}&=1-\frac{1}{5}-\frac{1}{6}=\frac{30-6-5}{30}\\&=\frac{19}{30}\end{aligned}$

New Ratio will be combined share $\times$ Old Ratio

A’s share

$=\frac{1}{2} \times \frac{19}{30}$$=\frac{19}{60}$

B’s share

$=\frac{1}{2} \times \frac{19}{30}$$=\frac{19}{60}$

Thus, new profit-sharing ratio will be:

$=\frac{19}{60}: \frac{19}{60}: \frac{1}{5}: \frac{1}{6}$

$\begin{aligned}&=\frac{19: 19: 12: 10}{60}\\&=19: 19: 12: 10\end{aligned}$

Thus, the  New profit-sharing ratio becomes 19 : 19 : 12 : 10

6.

Old Ratio of A and B is 3:2.

C’s share would be 1/4th of profit

Combined share of A and B

$\begin{array}{l}=1-\frac{1}{4} \\=\frac{3}{4}\end{array}$

New Ratio for A and B will be: Combined share of A and B $\times \frac{1}{2}$

$=\frac{3}{4} \times \frac{1}{2}=\frac{3}{8}$

=  ¾*1/2= 3/8

New Profit-sharing ratio will be

$=\frac{3}{8}: \frac{3}{8}: \frac{1}{4}$

$\begin{aligned}&=\frac{3: 3: 1}{8}\\&=3: 3: 2\end{aligned}$

Thus, the  New profit-sharing ratio becomes 3 : 3 : 2

Answer 2

Explanation:

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