Question

X and Y are partners in a firm sharing profits in the ratio of 5 : 3. They admitted Z as a new partner. The new profit-sharing ratio will be 4 : 3 : 2. The firm’s goodwill on Z’s admission was valued at ₹ 1,26,000. But Z could not bring any amount of goodwill in Cash. Credit will be given to ______.

Options

• X ₹ 17,500; Y ₹ 10,500

• X ₹ 16,000; Y ₹ 12,000

• X ₹ 22,750; Y ₹ 5,250

• X ₹ 1,02,375; Y ₹ 23,625

Answer 1

X and Y are partners in a firm sharing profits in the ratio of 5 : 3. They admitted Z as a new partner. The new profit-sharing ratio will be 4 : 3 : 2. The firm’s goodwill on Z’s admission was valued at ₹ 1,26,000. But Z could not bring any amount of goodwill in Cash. Credit will be given to X ₹ 22,750; Y ₹ 5,250.

Explanation:

Calculate the sacrificing Ratio:

X’s Sacrifice = `5/8 - 4/9`

= `(5 xx 9)/(8 xx 9) - (4 xx 8)/(9 xx 8)`

= `45/72 = 32/72`

= `13/72`

Y’s Sacrifice = `3/8 - 3/9`

= `(3 xx 9)/(8 xx 9) - (3 xx 8)/(9 xx 8)`

= `27/72 = 24/72`

= `3/72`

The sacrificing Ratio of X and Y = `13/72 : 3/72` or 13 : 3

The total goodwill of the firm is ₹ 1,26,000. Z’s share of profits is `2/9`.

Z’s Goodwill = `1,26,000 xx 2/9`

= 28,000

The ₹ 28,000 (adjusted via Z’s capital account) is distributed to X and Y in their sacrificing ratio of 13 : 3.

Amount credited to X = `28,000 xx 13/16`

= 22,750

Amount credited to Y = `28,000 xx 3/16`

= 5,250