A, B and C were partners in a firm sharing profits in the ratio 4 : 3 : 2. B retires from the firm and A and C decide to share the profits in the ratio 3 : 2. The gaining ratio is :

7 : 8

The correct answer is Option (1) → 7 : 8

The gaining ratio is,

Gaining ratio = New ration - old ratio

A's gain = New share - Old share

$=\frac{3}{5}-\frac{4}{9}=\frac{7}{45}$

C's gain = New share - Old share

$=\frac{2}{5}-\frac{2}{9}=\frac{8}{45}$

$∴\frac{A}{C}=\frac{\frac{7}{45}}{\frac{8}{45}}=\frac{7}{8}$