Question

Old ratio A :B:C=4:3:2 B retired and his share was taken by A :C equally find gaining ratio.

Answer 1

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 = 1 : 1