Question

(II) A, B, C and D are in partnership sharing profits and losses in the ratio of 36 : 24 : 20 : 20 respectively. E joins the partnership for 20% share, A, B, C and D would in future share profits among themselves as 3/10 : 4/10 : 2/10 and 1/10. Calculate the new profit sharing ratio after E’s admission. find sacrificing ratio​

Answer 1

Answer:

New Profit Sharing Ratio :

A : B : C : D : E = 6 : 8 : 4 : 2 : 5

and Sacrificing Ratio :

A : C : D = 3 : 1 : 3

Explanation:

Solution :

Old Ratio :

A : B : C : D = 36 : 24 : 20 : 20

• A's Share = $\dfrac{36}{100}$

• B's Share = $\dfrac{24}{100}$

• C's Share = $\dfrac{20}{100}$

• D's Share = $\dfrac{20}{100}$

E joins the partnership for 20% share,

• E's Share = $\dfrac{20}{100}$

Let,

Total Profit of all Partners = 1

• E's Share = $\dfrac{20}{100}$

Remaining Share =

$1 \: - \: \dfrac{20}{100} \: = \: \dfrac{80}{100}$

• A, B, C and D would in future share profits among themselves as 3/10 : 4/10 : 2/10 and 1/10

★ New Profit Sharing Ratio :

• A's New Share =

$\dfrac{3}{10} \: \times \: \dfrac{80}{100} \: = \: \dfrac{240}{1000} \: = \: \dfrac{24}{100}$

• B's New Share =

$\dfrac{4}{10} \: \times \: \dfrac{80}{100} \: = \: \dfrac{320}{1000} \: = \: \dfrac{32}{100}$

• C's New Share =

$\dfrac{2}{10} \: \times \: \dfrac{80}{100} \: = \: \dfrac{160}{1000} \: = \: \dfrac{16}{100}$

• D's New Share =

$\dfrac{1}{10} \: \times \: \dfrac{80}{100} \: = \: \dfrac{80}{1000} \: = \: \dfrac{8}{100}$

• E's Share =

$\dfrac{20}{100}$

★ New Profit Sharing Ratio :

• A : B : C : D : E

• $\dfrac{24}{100} : \dfrac{32}{100} : \dfrac{16}{100} : \dfrac{8}{100} : \dfrac{20}{100}$

24 : 32 : 16 : 8 : 20 = 6 : 8 : 4 : 2 : 5

New Profit Sharing Ratio :

A : B : C : D : E = 6 : 8 : 4 : 2 : 5

★ Sacrificing Ratio :

Sacrificing Ratio = Old Ratio - New Ratio

• A =

$\dfrac{36}{100}\: - \:\dfrac{6}{25} \:= \: \dfrac{(36 \: - \: 24)}{100} =\dfrac{12}{100} \:--- (Sacrifice)$

• B =

$\dfrac{24}{100} - \dfrac{8}{25} = \dfrac{(24 \: - \: 32) }{100} = \dfrac{ - \: 8}{ \: 100} \: - - \: (Gain)$

• C =

$\dfrac{20}{100} - \dfrac{4}{25} = \dfrac{(20 \: - \: 16)}{100} = \dfrac{4}{100} \: - - \: (Sacrifice)$

• D =

$\dfrac{20}{100} - \dfrac{2}{25} = \dfrac{(20 \: - \: 8)}{100} \: = \dfrac{12}{100} \: - - \: (Sacrifice)$

★ Sacrificing Ratio :

• A : C : D

• $\dfrac{12}{100} : \dfrac{4}{100} : \dfrac{12}{100}$

12 : 4 : 12 = 3 : 1 : 3

Sacrificing Ratio :

A : C : D = 3 : 1 : 3

Therefore,New Profit Sharing Ratio :

A : B : C : D : E = 6 : 8 : 4 : 2 : 5

and Sacrificing Ratio :

A : C : D = 3 : 1 : 3

Answer 2

Given :- A, B, C and D are in partnership sharing profits and losses in the ratio of 36 : 24 : 20 : 20 respectively. E joins the partnership for 20% share, A, B, C and D would in future share profits among themselves as 3/10 : 4/10 : 2/10 and 1/10.

To Find :- Calculate the new profit sharing ratio after E’s admission. find sacrificing ratio ?

Solution :-

→ Initial profit ratio A : B : C : D = 36 : 24 : 20 : 20 .

now, E joins the partnership for 20% share . since E takes 20% profit rest 80% profit will be distributed in the ratio of thier initial profit because profit ratio is same as investment ratio .

given that, A, B, C and D would in future share profits among themselves as 3/10 : 4/10 : 2/10 and 1/10.

so,

→ New profit of A = (3/10) * 80 = 24%

→ New profit of B = (4/10) * 80 = 32% .

→ New profit of C = (2/10) * 80 = 16% .

→ New profit of D = (1/10) * 80 = 8% .

then,

→ New profit ratio after E's admission will be = A : B : C : D : E = 24% : 32% : 16% : 8% : 20% = 6 : 8 : 4 : 2 : 5 (Ans.)

now,

→ Initial Profit of A = 36/(36 + 24 + 20 + 20) = (36/100)

→ Final profit of A = 24/(24 + 32 + 16 + 8 + 20) = (24/100)

then,

→ Sacrificing ratio = (36/100) - (24/100) = (12/100) = (3/25)

and,

→ Initial Profit of B = 24/100

→ Final profit of B = 32/100

since,

→ 32/100 > 24/100 .

then,

→ Gain ratio = (32/100) - (24/100) = (8/100) = (2/25) .

and,

→ Initial Profit of C = 20/100

→ Final profit of C = 16/100

then,

→ Sacrificing ratio = (20/100) - (16/100) = (4/100) = (1/25) .

and,

→ Initial Profit of D = 20/100

→ Final profit of D = 8/100

then,

→ Sacrificing ratio = (20/100) - (8/100) = (12/100) = (3/25) .

since A , C and D sacrifice in their profit .

→ Sacrificing ratio of A : C : D = (3/25) : (1/25) : (3/25) = 3 : 1 : 3 (Ans.)

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