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

**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 capitals are multiplied by the respective time periods.

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) When investments are altered in the given period we need to take the changes into consideration while calculating their profits.

Suppose A and B started their business with Rs.5000 and Rs.10,000 respectively. If after three months A invested another Rs.5000 then we have to consider A's capital for the remaining period is Rs.10,000

So A: B = (5000 × 3 + 10,000 × 9) : 10,000 × 12 = 1,05,000 : 1,20,000 = 7 : 8

**3. Working and Sleeping Partners :**A partner who manages the business is known as a working partner and the on who simply invests the money is a sleeping partner.

Working partner takes salary. So profits can be divided in the capitals ratio after subtracting salary of the working partner.

Suppose A and B started a business with Rs.5000 and Rs.10,000. A is a working partner so takes 10% of the profit as salary. If the profit at the end of the year is Rs.3000, then

Capitals Ratio = 5000 : 10000 = 1 : 2

Salary of A = 10%(3000) = 300

Remaining profit = 3000 - 300 = 2700

Share of A = $300 + \dfrac{1}{3} \times 2700$ = Rs.1200

Share of B = $\dfrac{2}{3} \times 2700$ = Rs.1800