Question

A, B and C were partners in a firm sharing profits and losses in the ratio of 4:3:2. B retires and his share is taken up equally by A and C. calculate gaining ratio

Answer 1

Answer:

Old Ratio :

A:B:C = 4:3:2

A's Share = 4/9

B's Share = 3/9

C's Share = 2/9

After B retires,

B's Share taken up equally by A and C

B's Share acquired by A =

3/9 × 1/2 = 3/18

B's Share acquired by C =

3/9 × 1/2 = 3/18

New Ratio =

A's New Share =

4/9 + 3/18 = (8+3)/18

11/18

C's New Share =

2/9 + 3/18 = (4+3)/18

7/18

New Ratio = A : C = 11/18 : 7/18

Gaining Ratio= New Share Ratio - old Share Ratio

A's Gain = 11/18 - 4/9

3/18

C's Gain = 7/18 - 2/9

3/18

Gain Ratio =

A : C = 3/18 : 3/18

3 : 3 = 1 : 1

Hence, Gaining Ratio = A : C = 1 : 1

Answer 2

Answer:

Gaining Ratio = A : C = 1 : 1

Explanation:

Solution :

★ Old Ratio :

A : B : C = 4 : 3 : 2

• A's Share = $\dfrac{4}{9}$

• B's Share = $\dfrac{3}{9}$

• C's Share = $\dfrac{2}{9}$

B retires and his share is taken up equally by A and C.

• B's Share = $\dfrac{3}{9}$

• B's Share taken by A =

$\implies{\dfrac{3}{9} \times \dfrac{1}{2} = \dfrac{3}{18}}$

• B's Share taken by C =

$\implies{\dfrac{3}{9} \times \dfrac{1}{2} = \dfrac{3}{18}}$

★ New Profit Sharing Ratio :

New Ratio = Old Ratio + Share acquired from B

• New Share of A =

$\implies{\dfrac{4}{9} + \dfrac{3}{18} = \dfrac{(8 \: + \: 3)}{18}}$

$\implies{\dfrac{11}{18}}$

• New Share of C =

$\implies{\dfrac{2}{9} + \dfrac{3}{18} = \dfrac{(4 \: + \: 3)}{18}}$

$\implies{\dfrac{7}{18}}$

New Profit Sharing Ratio =

• A : C

$\implies{\dfrac{11}{18} : \dfrac{7}{18}}$

$\implies$ 11 : 7

Gaining Ratio = New Ratio - Old Ratio

• A =

$\implies{\dfrac{11}{18} - \dfrac{4}{9} = \dfrac{(11 \: - \: 8)}{18}}$

$\implies{\dfrac{3}{18}}$

• C =

$\implies{\dfrac{7}{18} - \dfrac{2}{9} = \dfrac{(7 \: - \:4) }{18}}$

$\implies{\dfrac{3}{18}}$

Gaining Ratio =

• A : C

$\implies{\dfrac{3}{18} : \dfrac{3}{18}}$

$\implies$ 3 : 3 = 1 : 1

Therefore, Gaining Ratio = A : C = 1 : 1