6 :- (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 takes 4/9 of C’s share and balance is taken by B. calculate the new profit sharing ratio and gaining ratio.
Solution :-
(a) Old ratio = 2:1:2:1
Y retires and W, X and Z decides to share profits and losses equally in future
Calculation of gaining ratio of W, X and Z
New ratio – old ratio
W = 1/3 – 2/6 = 0
X = 1/3 – 1/6 = 1/6
Z = 1/3 – 1/6 = 1/6
Thus, their gaining ratio is 0:1:1
(b) Old ratio = 4:3:2
C retires from the business
Calculation of new profit sharing ratio
A = 4/9 + (2/9 x 4/9) = 4/9 + 8/81 = 44/81
B = 3/9 + (2/9 x 5/9) = 3/9 + 10/81 = 37/81
Thus, their new profit sharing ratio is 44:37
Calculation of their gaining ratio
New ratio – old ratio
A = 44/81 – 4/9 = 8/81
B = 37/81 – 3/9 = 10/81
Thus, Gaining ratio of A and B is 4:5