question_answer

On 1st April, 2014, X and Y entered into partnership for sharing profits in the ratio of 4 : 3. They admitted Z as a new partner on 1st April, 2016 for l/5th share which she acquired equally from X and Y. X, Y and Z earned profits at a higher rate than the normal rate of return for the year ended 31st March, 2017. Therefore, they decided to expand their business. To meet the requirements of additional capital, they admitted W as a new partner on 1st April, 2017 for l/7th share in profits which he acquired from X and Y in 7 : 3 ratio. Calculate

(i) New profit sharing ratio of X, Y and Z for the year 2016-17.

(ii) New profit sharing ratio of X, Y, Z and W on W's admission.

Answer:

(i) Calculation of new profit sharing ratio of X, Y and Z for the year 2016-17 Z is admitted for \[\frac{1}{5}th\] share. Z Acquired Profit Share from X\[=\frac{1}{5}\times \frac{1}{2}=\frac{1}{10}\] Z Acquired Profit Share from Y \[=\frac{1}{5}\times \frac{1}{2}=\frac{1}{10}\] X's New Share = Old Share - Sacrificed Share Y's New Share = Old Share - Sacrificed Share \[=\frac{4}{7}-\frac{1}{10}=\frac{40-7}{70}=\frac{33}{70}\] New profit sharing ratio will be \[=\frac{33}{70}:\frac{23}{70}:\frac{1}{5}=\frac{33:23:14}{70}\] or 33 : 23 : 14 (ii) Calculation of new profit sharing ratio of X, Y, Z and W Old Ratio-33 : 23 : 14 W is admitted for \[\frac{1}{7}th\] share, which he acquired from X and Y in 7 : 3 ratio. W Acquired Share from X =\[\frac{1}{7}\times \frac{7}{10}=\frac{7}{70}\] W Acquired Share from Y =\[\frac{1}{7}\times \frac{3}{10}=\frac{3}{70}\] X?s New Share = \[\frac{33}{70}-\frac{7}{70}=\frac{26}{70}\] Y?s New Share =\[\frac{33}{70}-\frac{3}{70}=\frac{20}{70}\] New Ratio=\[\frac{26}{70}:\frac{20}{70}:\frac{14}{70}:\frac{1}{7}=\frac{26}{70}:\frac{20}{70}:\frac{14}{70}:\frac{10}{70}\] or 13 : 10 : 7 : 5