x,y and z are patners sharing profits in the ratio of 1/9 : 1/3 and 5/9. z retires and surrenders 3/4th of his share in favour of x and remaining in favour of y. calculate new ratio and gaining ratio.

Z's Share = 5/9

.

Now, X will get 3/4th of Z's Share and Y will get remaining (i.e. 1 - (3/4) = 1/4th) of Z's Share.

Gaining Ratio between X and Y = (3/4) : (1/4) = 3:1

.

So, X's Gaining Share = (5/9) * (3/4) = 5/12,

and, Y's Gaining Share = (5/9) * (1/4) = 5/36

.

Therefore,

X's New Share:

= X's Old Share + X's Gaining Share

= 1/9 + 5/12

= (1*4 + 5*3) / 36

= (4 + 15) / 36

= 19/36,

and,

Y's New Share:

= Y's Old Share + Y's Gaining Share

= 1/3 + 5/36

= (1*12 + 5) / 36

= (12 + 5) / 36

= 17/36

.

So, New Ratio = (19/36) : (17/36) = 19 : 17

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