Question

X,Y and Z are sharing profits and losses in the ratio of 4:3:2 . Z retires the new ratio of X and Y is 3:2 . Calculate the gain ratio.

Answer 1

Explanation:  

Old ratio:

X : Y : Z = 4 : 3 : 2  

X = 4/9

Y = 3/9

Z = 2/9

 

New profit sharing ratio:

X : Y = 3 : 2

X = 3/5

Y = 2/5

Gaining ratio = New ratio - Old ratio

X gaining ratio = 3/5 - 4/9  = 7/45

z gaining ratio = 2/5 - 3/9 = 3/45

gaining ratio of X and Y is 7 : 3

Answer 2

Explanation:

Solution :

★ Old Ratio :

X : Y : Z = 4 : 3 : 2

• X's Share = 4/9
• Y's Share = 3/9
• Z's Share = 2/9

Z retires,

The new ratio of X and Y is 3:2.

★ New Profit Sharing Ratio :

X : Y = 3:2

• X's New Share = 3/5
• Y's New Share = 2/5

★ Gaining Ratio = New Ratio - Old Ratio

• X's Gain =

= 3/5 - 4/9

= (27 - 20)/45

= 7/45

• Y's Gain =

= 2/5 - 3/9

= (18 - 15)/45

= 3/45

Gain Ratio =

• X : Y
• 7/45 : 3/45

= 7 : 3

Therefore, Gaining Ratio of X and Y = 7 : 3.