Question

A,B,C are partners sharing profits and losses in the ratio 1/2:1/3:1/6. They admitted D as a new partner for 1/6 share it was agreed that C would retain his original share. Calculate new profit sharing ratio and sacrificing ratio

Answer 1

Answer:

A's old share= 2/5

B's old share= 2/5

C's old share= 1/5

D is admitted for 1/6th share. C will retain his original share.

Hence, remaining share= 1- [1/6] - [1/5]

= 19/30

This remaining share will be shared by A and B in their old ratio, i.e, 2:2

A's new share= 2/4 * 19/30

= 38/120

B's new share= 2/4 * 19/30

= 38/120

New Profit sharing ratio= 38:38:24:20

= 19:19:12:10

Sacrificing ratio= old ratio- new ratio

A's sacrifice= 2/5- 19/60

= 5/60

B's sacrifice= 2/5- 19/60

= 5/60

Sacrificing ratio= 5:5= 1:1

[Note: since nothing is mentioned, we assume that only A and B have sacrificed since C retains his old share]

Explanation:

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Answer 2

Answer:

New Profit Sharing Ratio =

A : B : C : D = 12 : 8 : 5 : 5

and Sacrificing Ratio = A : B = 3 : 2

Explanation:

Solution :

★ Old Ratio :

• A = $\dfrac{1}{2} = \dfrac{3}{6}$

• B = $\dfrac{1}{3} = \dfrac{2}{6}$

• C = $\dfrac{1}{6} = \dfrac{1}{6}$

A : B : C = 3 : 2 : 1

• A's Share = $\dfrac{3}{6}$

• B's Share =$\dfrac{2}{6}$

• C's Share =$\dfrac{1}{6}$

They admit D for 1/6 th share

• D's Share =$\dfrac{1}{6}$

C retain his original Share

• C's original Share = $\dfrac{1}{6}$

Total Share of C and D =

$\dfrac{1}{6} + \dfrac{1}{6} = \dfrac{2}{6}$

Let,

Total Share of the firm = 1

Balance of Share remains for A and B =

$1 - \dfrac{2}{6} = \dfrac{4}{6} =(\dfrac{2}{3})$

Remaining Share divided into A and B in their old ratio 3 : 2

★ New Profit Sharing Ratio :

New Share = Old Share × Remaining Share

• A's New Share =

$\longrightarrow \: \dfrac{3}{5} \times \dfrac{2}{3} = \dfrac{6}{15}$

• B's New Share =

$\longrightarrow \: \dfrac{2}{5} \times \dfrac{2}{3} = \dfrac{4}{15}$

• C's Share =

$\longrightarrow \: \dfrac{1}{6}$

• D's Share =

$\longrightarrow \: \dfrac{1}{6}$

New Profit Sharing Ratio =

• A : B : C : D

• $\dfrac{6}{15} : \dfrac{4}{15} : \dfrac{1}{6} : \dfrac{1}{6}$

$\longrightarrow\: \dfrac{12}{30} : \dfrac{8}{30} : \dfrac{5}{30} : \dfrac{5}{30}$

$\longrightarrow$ 12 : 8 : 5 : 5

∴ New Profit Sharing Ratio =

A : B : C : D = 12 : 8 : 5 : 5

★ Sacrificing Ratio :

Sacrificing Ratio = Old Ratio - New Ratio

• A's Sacrifice =

$\longrightarrow{\dfrac{3}{6} \: - \: \dfrac{12}{30} \: = \: \dfrac{(15 \: - \: 12)}{30}}$

$\longrightarrow{\dfrac{3}{30}}$

• B's Sacrifice =

$\longrightarrow{\dfrac{2}{6} \: - \: \dfrac{8}{30} \: = \: \dfrac{(10 \: - \: 8)}{30}}$

$\longrightarrow{\dfrac{2}{30}}$

Sacrificing Ratio =

• A : B

• $\dfrac{3}{30} : \dfrac{2}{30}$

$\longrightarrow$ 3 : 2

∴ New Profit Sharing Ratio =

A : B : C : D = 12 : 8 : 5 : 5

and Sacrificing Ratio = A : B = 3 : 2