Question

A.B.C were partners in a firm sharing profits in 3:2:1 ratio. They admitted D for 10% profits. Calculate the new profit sharing ratio?​

Answer 1

Explanation:

Old Ratio =

A: B:C = 3:2:1

• A = 3/6
• B = 2/6
• C = 1/6

D = 10% profit

Suppose,

whole profit of firm = 1

1 - 10/100 = 90/100 (9/10)

New profit sharing ratio =

• New share of A =

= 3/6 × 9/10

= 27/60

• New share of B =

= 2/6 × 9/10

= 18/60

• New Share of C =

= 1/6 × 9/10

= 9/60

D's share =

= 1/10 = 6/60

New profit sharing ratio =

A : B : C : D = 27/60 : 18/60 : 9/60 : 6/60

= 27 : 18 : 9 : 6

= 9 : 6 : 3 : 2

Hence, New profit sharing ratio of A,B,C and D = 9 : 6 : 3 : 2

Answer 2

Answer:

The New Profit Sharing Ratio is

A : B : C : D = 9 : 6 : 3 : 2

Explanation:

Solution :

★ Old Ratio :

A : B : C = 3 : 2 : 1

• A = $\sf{\dfrac{3}{6}}$

• B = $\sf{\dfrac{2}{6}}$

• C = $\sf{\dfrac{1}{6}}$

They admitted D for 10%

Let,

Total Profit of all Partners in the firm = 1

• D's Share = 10%
• D = $\sf{\dfrac{10}{100}}$

★ Remaining Share =

$1 \: - \: \dfrac{10}{100} \: = \: \dfrac{90}{100} \: = \: \dfrac{9}{10}$

★ The New Profit Sharing Ratio :

• A's new share =

$\sf{\longrightarrow{\dfrac{3}{6} \: \times \: \dfrac{9}{10} \: = \: \dfrac{27}{60}}}$

$\sf{\longrightarrow{ \dfrac{27}{60}}}$

• B's new share =

$\sf{\longrightarrow{\dfrac{2}{6} \: \times \dfrac{9}{10} \: = \: \dfrac{18}{60}}}$

$\sf{\longrightarrow{\dfrac{18}{60}}}$

• C's new share =

$\sf{\longrightarrow{\dfrac{1}{6} \: \times \: \dfrac{9}{10} \: = \: \dfrac{9}{60}}}$

• D's share =

$\sf{\longrightarrow{ \dfrac{1}{10} \: = \: \dfrac{(1 \: \times \: 6)}{(10 \: \times \: 6)} \: = \: \dfrac{6}{60}}}$

$\sf{\longrightarrow{\dfrac{6}{60}}}$

The New Profit Sharing Ratio :

• A : B : C : D

• $\sf{\dfrac{27}{60} : \dfrac{18}{60} : \dfrac{9}{60} : \dfrac{6}{60}}$

$\longrightarrow$ 27 : 18 : 9 : 6 = 9 : 6 : 3 : 2

Therefore, the New Profit Sharing Ratio is A : B : C : D = 9 : 6 : 3 : 2