Gaining share of Continuing Partner =

The correct answer is Option (3) → New share - Old share

On retirement or death, the continuing partners take over the outgoing partner's share. What each one gains is the increase in his share: what he now gets minus what he had before. For example, if a partner's share rises from 2/5 to 1/2, he gains 1/2 − 2/5 = 1/10.

Old share − new share is the other way round: it gives the sacrifice an old partner makes on admission (sacrificing ratio). Adding the old and new shares, or the old share and a sacrifice, measures nothing.