$W, X, Y$ and $Z$ are partners sharing profits and losses in the ratio of $\frac{1}{3}, \frac{1}{6}, \frac{1}{3}$ and $\frac{1}{6}$ respectively. $Y$ retires and $W, X$ and $Z$ decide to share the profit and losses equally in future. Calculate gaining ratio.

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Solution

Old ratio (W, X, Y and Z) = 1/3:1/6:1/3:1/6 or 2 : 1 : 2 : 1
New ratio (W, X and Z) = 1 : 1 : 1
Gaining ratio = New ratio - Old ratio
W's gain = 1/3 - 2/6 = 2/6 - 2/6 = 0
X's gain = 1/3 - 1/6 = 2/6 - 1/6 = 1/6
Z's gain = 1/3 - 1/6 = 2/6 - 1/6 = 1/6
Gaining ratio = 0 : 1 : 1

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W,X,Y and Z are partners sharing profits and losses in the ratio of 13,16,13 and 16 respectively. Y retires and W,X and Z decide to share the profit and losses equally in future. Calculate gaining ratio.

Old ratio (W, X, Y and Z) = 1/3:1/6:1/3:1/6 or 2 : 1 : 2 : 1New ratio (W, X and Z) = 1 : 1 : 1Gaining ratio = New ratio - Old ratioW's gain = 1/3 - 2/6 = 2/6 - 2/6 = 0X's gain = 1/3 - 1/6 = 2/6 - 1/6 = 1/6Z's gain = 1/3 - 1/6 = 2/6 - 1/6 = 1/6Gaining ratio = 0 : 1 : 1

$W, X, Y$ and $Z$ are partners sharing profits and losses in the ratio of $\frac{1}{3}, \frac{1}{6}, \frac{1}{3}$ and $\frac{1}{6}$ respectively. $Y$ retires and $W, X$ and $Z$ decide to share the profit and losses equally in future. Calculate gaining ratio.

Old ratio (W, X, Y and Z) = 1/3:1/6:1/3:1/6 or 2 : 1 : 2 : 1
New ratio (W, X and Z) = 1 : 1 : 1
Gaining ratio = New ratio - Old ratio
W's gain = 1/3 - 2/6 = 2/6 - 2/6 = 0
X's gain = 1/3 - 1/6 = 2/6 - 1/6 = 1/6
Z's gain = 1/3 - 1/6 = 2/6 - 1/6 = 1/6
Gaining ratio = 0 : 1 : 1