Question

Radha and Rukmini are partners in a firm sharing profits in 3 : 2 ratio. They admitted Gopi as a new partner Radha surrendered $\frac{1}{3}$ of her share in favour of Gopi and Rukmini surrendered $\frac{1}{4}$ of her share in favour of Gopi. Calculate the new profit sharing ratio.

Answer 1

New partner's share if not given, then it is always total sacrifice of old partners.

Old profit sharing ratio of Radha and Rukmini = 3 : 2

Gopi's share = $\frac{1}{3}$ of Radha + $\frac{1}{4}$ of Rukmini

Radha's sacrifice = $\frac{1}{3}$ of $\frac{3}{5}=\frac{1}{3}\times \frac{3}{5}=\frac{3}{15}$

Rukmini's sacrifice = $\frac{1}{4}$ of $\frac{2}{5}=\frac{1}{4}\times \frac{2}{5}=\frac{2}{20}$

Radha's new share = $\frac{3}{5}-\frac{3}{15}=\frac{9-3}{15}=\frac{6}{15}$

Rukmini's new share = $\frac{2}{5}-\frac{2}{20}=\frac{8-2}{20}=\frac{6}{20}$

Gopi's share = $\frac{3}{15}+\frac{2}{20}=\frac{12+6}{60}=\frac{18}{60}$

New profit sharing ratio of Radha, Rukmini and Gopi

$\frac{6}{15}:\frac{6}{20}:\frac{18}{60}$

or $\frac{24}{60}:\frac{18}{60}:\frac{18}{60}$

or 24 : 18 : 18

or 4 : 3 : 3