This is the ratio of share acquired by the remaining partners, from the retiring partner.
Gaining ratio = New Profit sharing ratio – Old Profit sharing ratio [Gain=New share-Old share]
It is very interesting to note that in the above case, if the answer is in negative, the result is sacrifice. It is not always necessary that all the remaining partners gain; one or some partners can sacrifice also on retirement/death of a partner. The condition is, the total gain should be equal to the total of the share of the retiring/deceased partner and the sacrifice made by any partner.