Anika and Radhika are partners sharing profit in the ratio of 5 : 1. T

1.	Anika and Radhika are partners sharing profit in the ratio of 5 : 1. They decide to admit Sanika to the firm for 1/5th share. Calculate the Sacrifice ratio of Anika and Radhika.
Answer» Balance = 1 – share of new partner = \(1-\frac{1}{5}\) = \(\frac{4}{5}\) (Remaining share) New ratio = Old ratio x Balance of 1 Anika’s New ratio = \(\frac{5}{6}\times\frac{4}{5}=\frac{20}{30}\) Radhika’s New ratio = \(\frac{1}{6}\times\frac{4}{5}=\frac{4}{30}\) Sanika’s New ratio = \(\frac{1}{5}\times\frac{6}{6}=\frac{6}{30}\) (Making denominator equal) ∴ New Profit and Loss ratio = \(\frac{20}{30}:\frac{4}{30}:\frac{6}{30}\) = 20 : 4 : 6 i.e. 10 : 2 : 3 Sacrifice ratio = old ratio – New ratio Anika’s Sacrifice ratio = \(\frac{5}{6}-\frac{20}{30}=\frac{25-20}{30}=\frac{5}{30}\) Radhika’s Sacrifice ratio = \(\frac{1}{6}-\frac{4}{30}=\frac{5-4}{30}=\frac{1}{30}\) ∴ Sacrifice ratio = \(\frac{5}{30}:\frac{1}{30}\) = 5 : 1

Anika and Radhika are partners sharing profit in the ratio of 5 : 1. They decide to admit Sanika to the firm for 1/5th share. Calculate the Sacrifice ratio of Anika and Radhika.

Answer»

Balance = 1 – share of new partner = \(1-\frac{1}{5}\)

= \(\frac{4}{5}\) (Remaining share)

New ratio = Old ratio x Balance of 1

Anika’s New ratio = \(\frac{5}{6}\times\frac{4}{5}=\frac{20}{30}\)

Radhika’s New ratio = \(\frac{1}{6}\times\frac{4}{5}=\frac{4}{30}\)

Sanika’s New ratio = \(\frac{1}{5}\times\frac{6}{6}=\frac{6}{30}\) (Making denominator equal)

∴ New Profit and Loss ratio = \(\frac{20}{30}:\frac{4}{30}:\frac{6}{30}\) = 20 : 4 : 6 i.e. 10 : 2 : 3

Sacrifice ratio = old ratio – New ratio

Anika’s Sacrifice ratio = \(\frac{5}{6}-\frac{20}{30}=\frac{25-20}{30}=\frac{5}{30}\)

Radhika’s Sacrifice ratio = \(\frac{1}{6}-\frac{4}{30}=\frac{5-4}{30}=\frac{1}{30}\)

∴ Sacrifice ratio = \(\frac{5}{30}:\frac{1}{30}\) = 5 : 1