The ratio in which the old partners agree to give their share of profit in favor of the incoming partner is called:

When a new partner is admitted to a partnership firm, the existing partners have to surrender or sacrifice a portion of their profit share to accommodate the incoming partner.

Sacrificing Ratio represents the proportion in which the old partners agree to reduce their share of profit in favor of the new partner.

The formula is: Sacrificing Ratio = Old Share - New Share

For example, if Partner A's share reduces from $\frac{3}{5}$ to $\frac{2}{5}$ after admission, the sacrifice is $\frac{3}{5} - \frac{2}{5} = \frac{1}{5}$.

This ratio is particularly important for determining the compensation (goodwill) that the sacrificing partners should receive from the incoming partner, as they are giving up a part of their future profits.

The other options represent different concepts:

• Old Ratio: The sharing ratio before admission
• New Ratio: The sharing ratio after admission (including the new partner)
• Gaining Ratio: The ratio in which continuing partners gain when a partner retires

Correct Option: 3 (Sacrificing Ratio)