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Q.X and Y are partners. They share profits and losses in the ratio of 2 : 1. They admit Z into partnership by giving 1/4 th share in future profits. Calculate the new profit sharing ratio.

Bihar BsebBSEB Bihar Intermediate (Class-12) Commerce Board 2025Subjective· 2mImportance★★★★★
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Z takes 1/4; X and Y share the balance 3/4 in their old 2:1 ratio, giving X = 1/2, Y = 1/4, Z = 1/4, i.e. 2 : 1 : 1.

Step 1 — Share left for old partners after Z's admission:

Total = 1. Z's share = 1/4.

Remaining share for X and Y = 1 - 1/4 = 3/4.

Step 2 — Divide the remaining 3/4 between X and Y in their old ratio 2 : 1 (X = 2/3, Y = 1/3 of the balance):

PartnerCalculationNew Share
X3/4 x 2/36/12 = 1/2

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