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

(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

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

**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