Question

Singh, Gupta and Khan are partners in a firm sharing profits in 3 :2 : 3 ratio. They admitted Jain as a new partner. Singh surrendered $\frac{1}{3}$ of his share in favour of Jain, Gupta surrendered $\frac{1}{4}$ of his share in favour of Jain and Khan surrendered $\frac{1}{5}$ in favour of Jain. Calculate new profit sharing ratio.

Answer 1

Old profit sharing ratio of Singh, Gupta and Khan = 3 : 2 : 3

Singh's sacrifice = $\frac{1}{3}$ of $\frac{3}{8}$ $=\frac{1}{3}\times \frac{3}{8}=\frac{3}{24}$

Gupta's sacrifice = $\frac{1}{4}$ of $\frac{2}{8}$ $=\frac{1}{4}\times \frac{2}{8}=\frac{2}{32}$

Khan's sacrifice = $\frac{1}{5}$ of $\frac{3}{8}$ $=\frac{1}{5}\times \frac{3}{8}=\frac{3}{40}$

Singh's new share = $\frac{3}{8}-\frac{3}{24}=\frac{9-3}{24}=\frac{6}{24}$

Gupta's new share = $\frac{2}{8}-\frac{2}{32}=\frac{8-2}{32}=\frac{6}{32}$

Khan's new share = $\frac{3}{8}-\frac{3}{40}=\frac{15-3}{40}=\frac{12}{40}$

Jain's share = $\frac{3}{24}+\frac{2}{32}+\frac{3}{40}=\frac{60+30+36}{480}=\frac{126}{480}$

Hence, new share of Singh : Gupta : Khan : Jain

$\frac{6}{24}:\frac{6}{32}:\frac{12}{40}:\frac{126}{480}$

$\frac{120:90:144:126}{480}$

or 120 : 90 : 144 : 126

or 20 : 15 : 24 : 21