## Partnership

### Important Formulae

Ratio of Divisions of Gains:

1.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

2. 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

### General Tips

1. Partnership:

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

2. Working and Sleeping Partners:

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

Example 1:

A and B started a business in partnership investing Rs.20,000 and Rs.15,000 respectively. After six months, C joined them with Rs.20,000. What will be B's share in the total profit of Rs.25,000 earned at the end of 2 years from the starting of the business?

Solution:

A : B : C =(20000×24):(15000×24):(20000×18)

=>4 :3 :3

B's share =Rs.(25000×3/10)

= Rs.7500.

Example 2:

Arun, Kamal and Vinay invested Rs. 8000, Rs. 4000 and Rs. 8000 respectively in a business. Arun left after six months. If after eight months, there was a gain of Rs. 4005, then what will be the share of Kamal?

Solution:

Arun : Kamal : Vinay = (8,000 x 6) : (4,000 x 8) : (8,000 x 8)

Arun : Kamal : Vinay = 48 : 32 : 64

Arun : Kamal : Vinay = 3 : 2 : 4

Kamal's share = Rs.4005 *(2/9)= Rs. 890

Example 3:

A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. Calculate the share of B in the profit.

Solution

For managing, A received = 5% of Rs. 7400 = Rs. 370

Balance = Rs. (7400 - 370) = Rs. 7030

Ratio of their investments = (6500 x 6) : (8400 x 5) : (10000 x 3)

= 39000 : 42000 : 30000

= 13 : 14 : 10

B's share = Rs.7030*(14/37) = = Rs.2660

Example 3:

X and Y invested in a business. They earned some profit which they divided in the ratio of 2 : 3. If X invested Rs.40,000. the amount invested by Y is

Solution

Suppose Y invested Rs.y

Then, 40000 /y = 2 / 3

=> y=(40000×3 / 2)

=> y=60000