Question

X and Y are partners in a firm sharing profits and losses in the ratio of 9 : 6. A new partner Z is admitted. X surrenders `3/15`th share of his profit in favour of Z and Y `6/15`th of his share in favour of Z. Calculate new profit sharing ratio.

Answer 1

1. Individual Sacrifice by X and Y

Old Ratio of X and Y: 9 : 6 (which simplifies to 3 : 2)

X's Old Share: `9/15`

Y's Old Share: `6/15`

X's Sacrifice (`3/15` of his share):

`9/15 xx 3/15 = 27/225`

Y's Sacrifice (`6/15` of his share):

`6/15 xx 6/15 = 36/225`

2. Calculation of New Shares

Formula: New Share = Old Share − Sacrificed Share

X's New Share:

`9/15 - 27/225 = (135 - 27)/225 = 108/225`

Y's New Share:

`6/15 - 36/225 = (90 - 36)/225 = 54/225`

Z's New Share:

`27/225 + 36/225 = 63/225`

3. Simplifying the Ratio

The new base ratio is 108 : 54 : 63. All these numbers are divisible by 9:

X: `108/9 = 12`

Y: `54/9 = 6`

Z: `63/9 = 7`

The New Profit Sharing Ratio among X, Y, and Z is:

12 : 6 : 7