Question

X, Y and Z were partners sharing profits in the ratio 2 : 3 : 4 with effect from 1st January, 2023 they agreed to share profits in the ratio 3 : 4 : 5. Each partner's gain or sacrifice due to change in the ratio will be:

Options

• `X  "Gain"  1/36; Y  "Nil"; Z  "Sacrifice"  1/36`

• `X  "Sacrifice"  1/36; Y  "Nil"; Z  "Gain"  1/36`

• `X  "Gain"  1/36; Y  "Sacrifice"  1/36; Z  "Nil"`

• `X  "Sacrifice"  1/36; Y  "Gain"  1/36; Z  "Nil"`

Answer 1

`bb(X  "Gain"  1/36; Y  "Nil"; Z  "Sacrifice"  1/36)`

Explanation:

Given:

Old Profit Sharing Ratio of X, Y and Z = 2 : 3 : 4

New Profit Sharing Ratio = 3 : 4 : 5

Step 1: Calculate Old Shares

Total parts = 2 + 3 + 4 = 9

X's old share = `2/9`

Y's old share = `3/9`

Z's old share = `4/9`

Step 2: Calculate New Shares

Total parts = 3 + 4 + 5 = 12

X's new share = `3/12` = `1/4`

Y's new share = `4/12` = `1/3`

Z's new share = `5/12`

Step 3: Calculate Gain or Sacrifice

X:

Gain = New Share − Old Share

= `1/4` − `2/9`

= `(9 − 8)/36`

= Gain `1/36`

Y:

Gain = `1/3` −` 3/9`

= `1/3` − `1/3`

= Nil

Z:
Sacrifice = Old Share − New Share

= `4/9` − `5/12`

=` (16 − 15) / 36`

= Sacrifice `1/36`