  Question

$$P$$ and $$Q$$ are partners sharing profits in the ratio of $$3:2$$. They admit $$R$$, a new partner who acquired $$1/5^{th}$$ of his share from $$P$$ and $$4/25^{th}$$ share from $$Q$$. Calculate New Profit Sharing Ratio and Sacrificing Ratio.

Solution

Admission of a partner leads to the reconstitution of partnership. As a result of which there is a change in the profit sharing ratio among the partners. The new partner acquires his share from the existing partners.P and Q are the old partners sharing ratio. R is admitted as new partner and he is acquiring his share in a specified ration from the existing  partners. First we will calculate the new ratio of the partners.P= 3/5 - 1/5 = 2/5Q= 2/5- 4/25 = 6/25R= 1/5 + 4/25 = 9/25so the new ratio is 10:6:9Now we will calculate the sacrificing ratio= old ratio - new ratioP= 3/5- 2/5= 1/5Q=2/5-6/25 = 4/25So, the ratio in which they are giving up the share is the sacrificing ratio.Quantitative Aptitude

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