When two or more than two persons run a business jointly, they are called partners and the deal is known as partnership.

Ratio of Divisions of Gains:

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.

When investments are for different time periods,

then equivalent capitals are calculated for a unit of time by taking (capital x 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.

Working and Sleeping Partners:

A partner who manages the business is known as a working partner and the one who simply invests the money is a sleeping partner.

S, T and U enter into a business with Rs. 12000, Rs. 15000 and Rs. 18000 respectively for a period of 3 years. Then find the ratio of their profits at the end of 3 years.

a) 4 : 5 : 6                     b) 4 : 6 : 5                     c) 6 : 5 : 4                     d) 5 : 4 : 6           

Solution:

Profit ratio        P₁ : P₂ : P₃ = I₁T₁ : I₂T₂ : I₃T₃

Profit ratio of X, Y and Z = 12000 × 3 : 15000 × 3 : 18000 × 3 = 4 : 5 : 6.

Answer: a

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