Question

A and B are sharing profits in the ratio of 2 : 1. C is admitted for 25% share. Afterward,
D is admitted for 1/5th share. Calculate new profit sharing ratio.
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Answer 1

Answer:

Explanation:

Solution :

Old Ratio :

A : B = 2 : 1

• A's Share = $\dfrac{2}{3}$

• B's Share = $\dfrac{1}{3}$

C is admitted for 25% Share

C's Share = 25 % = $\dfrac{25}{100}$

C's Share = $\dfrac{25}{100}$ = $\dfrac{1}{4}$

Let,

Total Profit = 1

• C's Share = $\dfrac{1}{4}$

Remaining Share =

1 - $\dfrac{1}{4}$ = $\dfrac{3}{4}$

• A's New Share =

$\dfrac{3}{4} \times \dfrac{2}{3} = \dfrac{6}{12}$

• B's New Share =

$\dfrac{3}{4} \times \dfrac{1}{3} = \dfrac{3}{12}$

• C's Share =

$\dfrac{1}{4} = \dfrac{3}{12}$

Profit Sharing Ratio : (C is admitted)

• A : B : C

• $\dfrac{6}{12} : \dfrac{3}{12} : \dfrac{3}{12}$

⇒ 6 : 3 : 3 = 2 : 1 : 1

Afterward, D is admitted for 1/5th share

★ Share before D's admission :

• A = $\dfrac{2}{4}$

• B = $\dfrac{1}{4}$

• C = $\dfrac{1}{4}$

D is admitted for 1/5th share

So,

• D's Share = $\dfrac{1}{5}$

Let,

Total Profit = 1

Remaining Share =

$1 - \dfrac{1}{5} = \dfrac{4}{5}$

After D admitted

New Profit Sharing Ratio :

• A's New Share =

$\dfrac{4}{5} \times \dfrac{2}{4} = \dfrac{8}{20}$

• B's New Share =

$\dfrac{4}{5} \times \dfrac{1}{4} = \dfrac{4}{20}$

• C's New Share =

$\dfrac{4}{5} \times \dfrac{1}{4} = \dfrac{4}{20}$

• D's Share =

$\dfrac{1}{5} = \dfrac{4}{20}$

• A : B : C : D

• $\dfrac{8}{20} : \dfrac{4}{20} : \dfrac{4}{20} : \dfrac{4}{20}$

⇒ 8 : 4 : 4 : 4 = 2 : 1 : 1 : 1

∴

New Profit Sharing Ratio :

A : B : C = 2 : 1 : 1 (After C admitted)

A : B : C : D = 2 : 1 : 1 : 1 (After D admitted)