Question

Anju and Manju are partners in a firm sharing profits and losses in the ratio of 3:2. A new partner Seema is admitted. Anju surrenders 1/5th share of her profits and Manju 2/5th of her share in favor of Seema. Here, the new profit sharing ratio of the partners will be:
A.12:6:7
B.15:10:6
C.3:2:7
D.12:10:6

Answer 1

Hint: A partnership is a formal arrangement by two or more parties to manage and operate a business and share its profit. In a general partnership, each partner shares in the profit and risks of the loss. In a limited partnership, the only general partner takes the role and responsibilities while a limited partner can invest in the business without taking on active responsibilities and personal financial liabilities.
In this question, first, find the share amounts of Anju and Manju, which will become Seema’s share and find remaining shares of Anju and Manju in the partnership and find their ratios.

Complete step-by-step answer:
In this question, first, find the share amounts of Anju and Manju, which will become Seema’s share and find remaining shares of Anju and Manju in the partnership and find their ratios.
Given the share of Anju and Manju is in the ratio 3:2, therefore
Anju’s share \[ = \dfrac{3}{{3 + 2}} = \dfrac{3}{5}\]
Manju’s share \[ = \dfrac{2}{{3 + 2}} = \dfrac{2}{5}\]
Now,
Anju’s surrender of share in Seema’s favor \[ = \dfrac{3}{5} \times \dfrac{1}{5} = \dfrac{3}{{25}}\]
Manju’s surrender of share in Seema’s favor \[ = \dfrac{2}{5} \times \dfrac{2}{5} = \dfrac{4}{{25}}\]
Therefore Seema’s total share \[ = \dfrac{3}{{25}} + \dfrac{4}{{25}} = \dfrac{7}{{25}}\]
Hence remaining shares of Anju and Manju,
Anju’s new share= \[\dfrac{3}{5} - \dfrac{3}{{25}} = \dfrac{{15 - 3}}{{25}} = \dfrac{{12}}{{25}}\]
Manju’s new share= \[\dfrac{2}{5} - \dfrac{4}{{25}} = \dfrac{{10 - 4}}{{25}} = \dfrac{6}{{25}}\]
Therefore the new profit sharing ratio of the partners will be \[ = \dfrac{{12}}{{25}}:\dfrac{6}{{25}}:\dfrac{7}{{25}} = 12:6:7\]
So, the correct answer is “Option A”.

Note: Students should keep in mind that when the new partner purchases his profit from the old partners equally, then in such a case, the new profit sharing ratio of the old partners can be calculated by deducting the sacrifice made by them from their existing shares.