Step 1: When used.
Gaining ratio is used on \emph{retirement/death} of a partner or when remaining partners increase their shares.
Step 2: Compute for each partner.
For partner \(A\): \(G_A = N_A - O_A\), similarly for \(B\), etc. Positive result indicates gain; negative indicates sacrifice.
Step 3: Purpose.
To apportion goodwill/reserve adjustments and revaluation effects fairly among the gaining partners.
Final Answer:
\[
\boxed{\text{Gaining Ratio} = (\text{New Share} - \text{Old Share}) \text{ of each continuing partner}}
\]
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