Ques18

Q18. A, B and C are partners sharing in the ratio of 4 : 3 : 2. They admit D its 1/9 share. It is agreed that A would retain his original share. Calculate the new ratio and sacrificing ratios.

        [ Ans. New Ratio 20 : 12 : 8 : 5, Sacrificing Ratio between B and C 3 : 2]
 

Dear Student,

$$\begin{gathered} \mathrm{Let} \mathrm{Total} \mathrm{Profit} \mathrm{Share} \mathrm{be} 1 \\ \mathrm{D}\text{'}\mathrm{s} \mathrm{share}=\frac{1}{9} \\ \mathrm{A}\text{'}\mathrm{s} \mathrm{share}=\frac{4}{9}\left(\mathrm{retained}\right) \\ \mathrm{Remaining} \mathrm{share}=1-\frac{1}{9}-\frac{4}{9}=\frac{4}{9}(\mathrm{to} \mathrm{be} \mathrm{shared} \mathrm{between} \mathrm{B} \mathrm{and} \mathrm{C} \mathrm{in} \mathrm{their} \mathrm{old} \mathrm{ratio} \mathrm{i}.\mathrm{e}. 3:2) \\ \mathrm{B}\text{'}\mathrm{s} \mathrm{new} \mathrm{share}=\frac{4}{9}\times \frac{3}{5}=\frac{12}{45} \\ \mathrm{C}\text{'}\mathrm{s} \mathrm{new} \mathrm{share}=\frac{4}{9}\times \frac{2}{5}=\frac{8}{45} \\ \mathrm{New} \mathrm{Ratio}=\frac{4}{9}:\frac{12}{45}:\frac{8}{45}:\frac{1}{9} \mathrm{or} 20:12:8:5 \end{gathered}$$

Notes:
(a) Sacrifice ratio between B and C is 3:2. Since A has retained his share, this implies that he didn't sacrifice anything on D's admission. And since no information is given as to how D is acquiring 1/9 share from B and C, so it is assumed that B and C are sacrificing in their old profit sharing ratio i.e. 3:2.
(b) To verify, you can calculate sacrificing ratio for B and C as the difference between their old and new ratios.