It is the ratio in which the old partners sacrifice their share in favor of a new partner.
Sacrificing ratio = Old Profit sharing ratio – New Profit sharing ratio [Sacrifice=old share-new share]
It is very interesting to note that in the above case, if the answer is in negative, the result is Gain. It is not always necessary that all the old partners sacrifice; one or some partners can gain also on admission of a new partner. The condition is that the total sacrifice should be equal to the total of gain and the share of the new partner.