These are the important formulas for Partnership problems-
I. Partnership : When two or more than two persons run a business jointly, they are called partners and the deal is known as partnership.
II. Ratio of Division of Gains :
(i) When investments of all the partners are for the same time, the gain or loss is distributed among the partners in the ratio of their investments.
Suppose A and B invest Rs. x and Rs. y respectively for a year in a business, then at the end of the year :
(A’s share of profit) : (B’s share of profit) = x : y.
(ii) When investments are for different time periods, then equivalent capitals are calculated for a unit of time by taking (capital * number of units of time). Now, gain or loss is divided in the ratio of these capitals.
Suppose A invests Rs. x for p months and B invests Rs. y for q months, then (A’s share of profit) : (B’s share of profit) = xp : yq.
III. Working and Sleeping Partners : A partner who manages the business is known as working partner and the one who simply invests the money is a sleeping partner.