Question

(a) W, X, Y and Z are partners sharing profits and losses in the ratio of 1/3, 1/6, 1/3 and 1/6 respectively. Y retires and W, X and Z decide to share the profits and losses equally in future. Calculate gaining ratio.
(b) A, B and C are partners sharing profits and losses in the ratio of 4 : 3 : 2. C retires from the business. A is acquiring 4/9 of C’s share and balance is acquired by B. Calculate the new profit-sharing ratio and gaining ratio.

Answer 1

4/9)(3/9)(2/9)

Explanation:

you are going to add all the set if number and ten you are going to calculate all the numbers and you are going to get the answer for the question

Answer 2

The new profit-sharing ratio and gaining ratio are given below:

Explanation:

(a)

Old Ratio W, X, Y and Z

$=\frac{1}{3}: \frac{1}{6}: \frac{1}{3}: \frac{1}{6}$

Or

$\frac{2:1:2:1}{6}=2:1:2:1$

New Ratio (W, X and Z) = 1: 1: 1

New Ratio = New Ratio - Old Ratio

Calculation of Shares:

W's Share

$=\frac{1}{3}-\frac{2}{6}=\frac{2-2}{6}=Nil$

X's Share

$=\frac{1}{3}-\frac{1}{6}=\frac{2}{6}-\frac{1}{6}=\frac{1}{6}$

(Gain)

Z's share

$=\frac{1}{3}-\frac{1}{6}=\frac{2}{6}-\frac{1}{6}=\frac{1}{6}$

(Gain)

Therefore, the New Ratio =0: 1: 1

Thus, the gaining ratio of X, Y and Z will be 0 : 1 : 1

(b)

Old Ratio (A, B and C)=4: 3: 2

C's Profit Share = 2/9

A get by 4/9 of C's Share and remaining Share is get by B.

Share get by A

$=\frac{2}{9} \times \frac{4}{9}=\frac{8}{81}$

Share get by B = C's share - Share get by A

$=\frac{2}{9}-\frac{8}{81}=\frac{18}{81}-\frac{8}{81}=\frac{10}{81}$

Calculation of New Profit share:

New profit share = Old Profit share + share get from C

$A's=\frac{4}{9}+\frac{8}{81}=\frac{36}{81}+\frac{8}{81}=\frac{44}{81}$

$B's=\frac{3}{9}+\frac{10}{81}=\frac{27}{81}+\frac{10}{81}=\frac{37}{81}$

Therefore New Profit Ratio of A and B=44: 37

Calculation of Gaining Ratio:

Gaining Ratio = New Ratio- Old Ratio

$A's=\frac{44}{81}-\frac{4}{9}=\frac{44}{81}-\frac{36}{81}=\frac{8}{81}$

(Gain)

$B's=\frac{37}{81}-\frac{3}{9}=\frac{37}{81}-\frac{27}{81}=\frac{10}{81}$

(Gain)

Therefore, the Gaining Ratio

$=\frac{8: 10}{81}$  or 4: 5

Thus, the new profit sharing ratio and the gaining ratio will be 44 : 37 and 4 : 5 respectively.