Abhiram and Ragini are partners sharing profits in the ratio of 3:2. They admit Arun a new partner for 1/5th share in the future profits of the firm which he gets equally from Abhiram and Ragini. Calculate the new profit sharing ratio of Abhiram, Ragini and Arun.

Old ratio of Abhiram and Ragini = 3:2

Converting to fractions: Abhiram = $\frac{3}{5}$, Ragini = $\frac{2}{5}$

Arun is admitted for $\frac{1}{5}$th share, which he gets equally from both partners.

Sacrifice by each partner:

• Abhiram's sacrifice = $\frac{1}{5} \times \frac{1}{2} = \frac{1}{10}$
• Ragini's sacrifice = $\frac{1}{5} \times \frac{1}{2} = \frac{1}{10}$

New shares:

Abhiram's new share = $\frac{3}{5} - \frac{1}{10} = \frac{6}{10} - \frac{1}{10} = \frac{5}{10}$

Ragini's new share = $\frac{2}{5} - \frac{1}{10} = \frac{4}{10} - \frac{1}{10} = \frac{3}{10}$

Arun's share = $\frac{1}{5} = \frac{2}{10}$

New profit sharing ratio = $\frac{5}{10} : \frac{3}{10} : \frac{2}{10}$

= 5:3:2