Q.Praveena and Dhanya are sharing profits in the ratio of 7 : 3. They admit Malini into the firm. The new ratio among Praveena, Dhanya and Malini is 5 : 2 : 3. Calculate the Sacrificing ratio.

The Sacrificing Ratio is the ratio in which the old partners give up part of their former profit share to make room for the new partner. For each old partner, Sacrificing Share = Old Share − New Share; the ratio of these sacrificing shares to each other is the Sacrificing Ratio. It is used specifically to divide the premium for goodwill that the new partner pays (whether in cash or through a capital-account adjustment) among the old partners — never the old ratio and never the new ratio, unless one of them happens to coincide with it. The sacrificing ratio can equal the old ratio (when the new partner's share is simply carved proportionately out of the old shares), but …