Q.Apte and Bhate are sharing profits and losses in the ratio 3 : 2, if Kate is admitted at 1/4 share then calculate new profit sharing ratio.

Kate's share = 1/4. The balance 3/4 is divided between Apte and Bhate in their old ratio 3:2. Converting to a common denominator gives Apte : Bhate : Kate = 9 : 6 : 5.

Method: New shares of old partners = Remaining share × their old ratio.

The term is the Sacrifice Ratio (Sacrificing Ratio).

On admission of a partner, the existing partners surrender a portion of their profit share to the incoming partner. The proportion each old partner gives up is the Sacrificing Ratio, calculated as:

Sacrifice Ratio = Old Ratio − New Ratio.

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