Question

X, Y, Z are partners in a firm with profit sharing ratio of 3 : 1 : 1. They admitted R as a new partner for `1/4`th share in profits. R brings ₹ 2,25,000 as his share of goodwill.

JOURNAL
Date	Particulars	L.F.	Dr. (₹)	Cr. (₹)
	Premium for Goodwill A/c   ...Dr.		2,25,000
	Y's Capital A/c   ...Dr.		90,000
	To X's Capital A/c			2,70,000
	To Z's Capital A/c			45,000
	(Goodwill credited to old partners in their sacrificing ratio)

Calculate new profit sharing of X : Y : Z : R.

Answer 1

Based on R’s share of premium for goodwill, total goodwill of the firm
\[= ₹2,25,000 \times \frac{4}{1} = ₹9,00,000\]

Since Y’s Capital A/c has been debited, it means he has also gained and his gained share is $\frac{90,000}{9,00,000} = \frac{1}{10}$

Total gain of Y and new partner R $= \frac{1}{10} + \frac{1}{4} = \frac{2 + 5}{20} = \frac{7}{20}$

Sacrifice ratio of X and Z $= ₹2,70,000 : ₹45,000 = 6 : 1$

Sacrifice made by X $= \frac{7}{20} \times \frac{6}{7} = \frac{6}{20}$

Sacrifice made by Z $= \frac{7}{20} \times \frac{1}{7} = \frac{1}{20}$

New Profit share of X (Old Share – Sacrificed Share) $= \frac{3}{5} - \frac{6}{20} = \frac{6}{20}$

New Profit share of Y (Old Share + Gained Share) $= \frac{1}{5} + \frac{1}{10} = \frac{3}{10} \text{ or } \frac{6}{20}$

New Profit share of Z (Old Share – Sacrificed Share) $= \frac{1}{5} - \frac{1}{20} = \frac{3}{20}$

R’s Share $= \frac{1}{4} \text{ or } \frac{5}{20}$

New Profit Sharing Ratio of X, Y, Z and R $= 6 : 6 : 3 : 5$