Question

A and B are in partnership sharing profits and losses as 3 : 2. C is admitted for 1/4th share. Afterwards D enters for 20 paise in the rupee. Compute profit-sharing ratio of A, B, C and D after D admission.

Answer 1

New Profit-sharing ratio is calculated below.

Explanation:

Profit and Loss sharing ratio between A:B is given as 3:2

C’s share of profit after his admission = 1/4th of the profit

Calculating combined share of A, B after C’s admission = 1- C’s share

= 1- ¼ = ¾  

Calculation of New Ratio:

New Ratio = Old Ratio $\times$ Combined share of A,B,C, D  

A’s new share

$=\frac{3}{5} \times \frac{3}{4}=\frac{9}{20}$

B’s new share

$=\frac{2}{5} \times \frac{3}{4}=\frac{6}{20}$

New profit-sharing ratio of A, B and C becomes

$=\frac{9}{20}: \frac{6}{20}: \frac{1}{4}=9: 6: 5$

New Profit sharing rato after C's admission will be treated as old rato to determine the ratio after D's admission. Old Ratio (I.e. before D's admission) between A, B and C =9: 6: 5

Now, D’s admission with share of 20/100 of profit

Calculating combined share of A, B, C after D’s admission = 1- D’s share

$=1-\frac{20}{100}=\frac{80}{100}$

Calculation of New shares:

New Ratio = Old Ratio $\times$ Combined share of A, B, C, D  

A’s new share

$=\frac{9}{20} \times \frac{80}{100}=\frac{72}{200}$

B’s new share

$=\frac{6}{20} \times \frac{80}{100}=\frac{48}{200}$

C’s new share

$=\frac{5}{20} \times \frac{80}{100}=\frac{40}{200}$

After D’s admission, ratio becomes

$=\frac{72}{200}: \frac{48}{200}: \frac{40}{200}: \frac{20}{100}=9: 6: 5: 5$