Partnership

gaining ratio is used when partners existing in business get more profit than they would get before the event in question takes place, i.e. a death of a partner or retirement of a partner. the amount of profit that should have gone to the dead or retired profit will now go to the remaining partners as such they have gained in profit the amount of profit they gain when represented in the form of ratio will give gaining ratio. sacrificing ratio is used when partners in business get less profit than they would get before the event in question takes place i.e., joining of  anew partner. the profits which the new partner is given would have gone to the old partners if the new partner hasn't joined the partnership as such they are sacrificing a share of their profits to the new partner. the ratio in which they are sacrificing the profits (i.e. the amount they would have gotten additionally hadn't the new partner joined the partnership represented in the form of ratio) is the sacrificing ratio.

old profit sharing ratio is applied to distribute reserves and surplus which should be disrtributed to the partners(reserves and surplus are undistributed profits and as such should be distributed to the existing partners before the composition of firm changes). also revaluation profit or loss should be distributed to the partners in old profit sharing ratio. goodwill not being an asset which is displayed in the balance sheet should be credited to the retiree or dead person and debited to existing partners in gain ratio, and should be credited to existing partners and debited to incoming new partner in the sacrificing ratio . Also when you carry out revaluation and do not want to show the assets at their new value and carry the assets at old value, the share of the partner, going out (i.e. dead or retired) should be debited to the remaing partners accounts in gaining ratio. (basically a thumb rule is if it is something present in the balance sheet we have to use old profit sharing ratio to distribute it to all partners and when you credit or debit one partner and debit or credit respectivlely all the other partners and if it is not something present in the balance sheet you should use the gaining or sacrificing ratio)

When there s reconstitution in partnership ie , changes in profit sharing ratio , or at the time of retirement or death of a partner , the partners who gains should compensate the losing partner in gaining ratio. ie share of goodwill of losing or outgoing partner should beared by gaining partners in the gaining ratio.

At the time of admission the existing partners have to make sme sacrifices . The new partner should bring the share of goodwill to compensate sacrificing partners .The sacrificing partners divide the goodwil bought by new partner among themselves in sacrificing ratio . 

The Gaining Ratio & Sacificing Ratio are used to divide goodwill .

The Old Ratio is used to divide the accumulated profits nd revaluation profit / loss among the old partners before the changes made in partnershp. 

regards , 
Arun Anton Ashok