Q.X and Y share profits equally. They admit Z into partnership for 1/4 share. It is agreed that the new profit-sharing ratio of X, Y and Z will be 2:1:1. Calculate the sacrificing ratio.

The sacrificing ratio is Old Share minus New Share for each partner — here it turns out X sacrifices nothing at all, and only Y sacrifices, even though both held an equal old share.

X: old 1/2 − new 1/2 (2/4) = 0. Y: old 1/2 − new 1/4 = 1/4, which exactly equals Z's incoming 1/4 share.

Old ratio: X = 1/2, Y = 1/2 (since X and Y share equally).

New ratio 2:1:1 means, out of a total of 4 parts, X = 2/4 = 1/2, Y = 1/4, Z = 1/4.

Sacrificing Ratio = Old Share − New Share, for each partner:

X: 1/2 − 1/2 = 0 — X's share is exactly unchanged, so X makes NO sacrifice at all.

Y: 1/2 − 1/4 = 1/4 — Y alone gives up 1/4 of his old share.

Check: the total sacrifice made (0 + 1/4 = 1/4) must exactly equal the new partner's incoming share; Z's share is indeed 1/4, so the figures are internally consistent.

Since X makes no sacrifice, X will receive NO share of any premium for goodwill Z brings in — the entire premium will go to Y, who is the only partner who has actually sacrificed.

A common error is assuming the sacrificing ratio must automatically follow the old profit-sharing ratio (here, equally, 1:1) whenever a numeric example doesn't explicitly say otherwise — whenever the NEW ratio is given directly, the sacrificing ratio must always be freshly computed as Old Share minus New Share for each partner, and it can turn out very different from the old ratio, as this example shows.