Question

X, Y and Z are partners sharing profit in the ratio of 1/9 : 1/3 and 5/9. Z retires and surrenders 3/4th of this share in favour of X and remaining in favour of Y. Calculate new ratio and gaining ratio.

Answer 1

Old ratio:

`X : Y : Z = 1/9 : 1/3 : 5/9 = 1 : 3 : 5`

Z's share = `5/9`

Gain of X

X gets `3/4` of Z's share:

`3/4 xx 5/9 = 5/12`

Gain of Y

Y gets the remaining `1/4`:

`1/4 xx 5/9 = 5/36`

Therefore, gaining ratio:

`5/12 : 5/36 = 3 : 1`

New Ratio

X's new share:

`1/9 + 5/12 = 19/36`

Y's new share:

`1/3 + 5/36 = 17/36`

New Profit-Sharing Ratio = 19 : 17

Gaining Ratio = 3 : 1