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 :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 7 : 8
The gaining ratio is the ratio of the shares gained by the remaining partners:
Gain = New share − Old share
Old shares: A \(\frac{4}{9}\), C \(\frac{2}{9}\). New shares: A \(\frac{3}{5}\), C \(\frac{2}{5}\).
\( \displaystyle \text{A's gain} = \frac{3}{5} - \frac{4}{9} = \frac{27 - 20}{45} = \frac{7}{45} \)
\( \displaystyle \text{C's gain} = \frac{2}{5} - \frac{2}{9} = \frac{18 - 10}{45} = \frac{8}{45} \)
So the gaining ratio of A and C is 7 : 8.
(3 : 2 is the new profit-sharing ratio, not the gaining ratio.)