Question

Arun, Bhushan and Chetan are partners in a firm sharing profits in 3 : 2 : 3 ratio. They decide to admit Sehzad as a partner, who is associated with them as their selling agent for the last 10 years. Arun surrendered $\frac{1}{3}$ of his share in favour of Sehzad. Bhushan surrendered $\frac{1}{4}$ of his share in favour of Sehzad and Chetan surrendered $\frac{1}{5}$ of his share in favour of Sehzad. (i) Calculate new profit sharing ratio, and (ii) Highlight the values in admitting Sehzad.

Answer 1

Calculation of Surrendered share:

Arun's old share $=\frac{3}{8}$, Arun surrenders $\frac{1}{3}$ of $\frac{3}{8}$ in favour of Sehzad, i.e., $\frac{1}{3}\times \frac{3}{8}=\frac{1}{8}$

Bhushan's old share $=\frac{2}{8}$, Bhushan surrenders $\frac{1}{4}$ of $\frac{2}{8}$ in favour of Sehzad, i.e.,

$\frac{1}{4}\times \frac{2}{8}=\frac{1}{16}$

Chetan's old share $=\frac{3}{8}$, Chetan surrenders $\frac{1}{5}$ of $\frac{3}{8}$ in favour of Sehzad, i.e.,

$\frac{1}{5}\times \frac{3}{8}=\frac{3}{40}$

Calculation of New Ratios:

Arun's new share after surrendenring $\frac{1}{8}$ in favour of Sehzad

$=\frac{3}{8}-\frac{1}{8}=\frac{2}{8}$

Bhushan's new share after surrendering $\frac{1}{16}$ in favour of Sehzad

$=\frac{2}{8}-\frac{1}{16}=\frac{4-1}{16}=\frac{3}{16}$

Chetan's new share after surrendering $\frac{3}{40}$ in favour of Sehzad

$=\frac{3}{8}-\frac{3}{40}=\frac{15-3}{40}=\frac{12}{40}$

Sehzad's share is the total of $\frac{1}{8}$ from Arun, $\frac{1}{16}$ from Bhushan and $\frac{3}{40}$ from Chetan

$=\frac{1}{8}+\frac{1}{16}+\frac{3}{40}=\frac{10+5+6}{80}=\frac{21}{80}$

Hence, New Ratio of Arun, Bhushan, Chetan and Sehzad

$=\frac{2}{8}:\frac{3}{16}:\frac{12}{40}:\frac{21}{80}=\frac{20:15:24:21}{80}=20:15:24:21$

(ii) Values:

(a) Secularism: By admitting a partner from different religion.

(b) Loyalty : By recognising the services provided by Sehzad as their agent in the past.