Discussion
X and Y are partners sharing profits in the ratio of 3 : 1. They admit Z as a partner who pays ₹ 4,000 as goodwill. The new profit ratio being 2 : 1 : 1 among X, Y and Z respectively. The amount of goodwill will be credited to ................. .
Answer: B
The goodwill is credited to X only.
Goodwill brought in by a new partner goes to the old partners in their sacrificing ratio, the old share minus the new share:
\[ \begin{aligned} X &= \tfrac{3}{4} - \tfrac{2}{4} = \tfrac{1}{4} \\ Y &= \tfrac{1}{4} - \tfrac{1}{4} = 0 \end{aligned} \]
Y keeps the same quarter share, so only X sacrifices, and the whole ₹ 4,000 is credited to X.
Splitting it 3,000 and 1,000 uses the old ratio instead of the sacrificing ratio, and 2,500 and 1,500 has no basis in either ratio. Y alone sacrificed nothing, so 'Y only' is wrong.
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