Question

Murli, Vijay and Sagar are are partners sharing profits in the ratio of 3 : 2 : 1. Rajni is admitted as a partners for `1/5`th share in profits. Murli sacrifices `3/20` from his share in favour of Rajni and rest of the sacrifice was made by Vijay and Sagar in their old profit ratio. Ascertain sacrifice ratio and new profit sharing ratio.

Answer 1

1. Calculation of Sacrifice Ratio:

Sacrificed Share of Murli \[= \frac{3}{20}\]

Remaining share of Rajni i.e., $\frac{1}{5} - \frac{3}{20} = \frac{1}{20}$ will be provided by Vijay and Sagar in their old ratio of $2 : 1$.

Therefore, Sacrificed share of Vijay $= \frac{2}{3} \text{ rd of } \frac{1}{20} = \frac{1}{30}$

Sacrificed share of Sagar $= \frac{1}{3} \text{ rd of } \frac{1}{20} = \frac{1}{60}$

$\therefore$ Sacrifice by Murli, Vijay and Sagar is $= \frac{3}{20} : \frac{1}{30} : \frac{1}{60}$

$= \frac{9 : 2 : 1}{60} \text{ or } 9 : 2 : 1$

2. Calculation of New Profit Sharing Ratio:

New Profit Share $= \text{Old Profit Share} - \text{Sacrificed Share}$

Murli’s New Profit Share $= \frac{3}{6} - \frac{3}{20} = \frac{30 - 9}{60} = \frac{21}{60}$

Vijay’s New Profit Share $= \frac{2}{6} - \frac{1}{30} = \frac{20 - 2}{60} = \frac{18}{60}$

Sagar’s New Profit Share $= \frac{1}{6} - \frac{1}{60} = \frac{10 - 1}{60} = \frac{9}{60}$

Rajni’s Share $= \frac{1}{5} \quad\quad\quad\quad \text{ or } \frac{12}{60}$

$\therefore$ New Profit Sharing ratio of Murli, Vijay, Sagar and Rajni is $= 21 : 18 : 9 : 12$ $\text{Or } 7 : 6 : 3 : 4$