Partnership

When two or more persons make an association and invest money for running a certain business and after certain time receive profit in the ratio of their invested money and time period of investment, then such an association is called partnership and the persons involved in the partnership
are called partners.

Partnership is of Two Types

1.Simple Partnership
If all partners invest their different capitals (money) for the same time period or same capital for different time period then their profit or loss is in the ratio of their investments or time period of investment then such a partnership is called simple partnership.

2. Compound Partnership
If all partners invest their different capitals (money) for different time period, then their profit not only depends on their investments but also on the time period of their investment, then such a partnership is called compound partnership.

Important formulas:

1. If the investment made by the partners is for same time, then the profit or loss is shared among the partners in the ratio of their investments.

E.g. If A & B invest Rs.x & 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. If the investment is made for different time periods, then the gain or loss is calculated in the ratio of the equivalent capitals (i.e. equivalent capital = capital x time of investment).
E.g. If A invests Rs.x for p months & B invests Rs.y for q months, then
(A’s share of profit) : (B’s share of profit) = xp : yq

Partners are of Two Types

1. Active or Working Partner

A partner who not only invests money, but also take part in the business activities for which hedraws a defined salary or gets some share from profit before its division is called an active partner.

2. Sleeping Partner

A partner who only invests money and does not take part in business activities is called sleeping partner

Example1:. Raj and Sanjay are partners in a business firm. Raj puts in Rs. 5000 and Sanjay put in Rs. 6000. Raj receives 12 1/2 % of the profit for managing the business and the balance is divided in the ratio of their capitals. If the total profit is Rs. 880, find Raj’s total share.

A. Rs. 470           B. Rs. 465                    C. Rs. 460                   D. Rs. 455

SOLUTION:

As Raj is managing the business he is the working partner, while Sanjay is the sleeping partner. Raj gets his share of profit and 12.5 % for managing the business.
12.5 % of 880 is 110.
So, Raj gets Rs. 110 and the other profit as well.
This profit will be based on the ratio of their investment.
Their investment is in the ratio of 5: 6. Thus, the share of Raj in profit is (5/11 x 770) = 350.
So, the total gain for Raj will be 110 + 350 = Rs. 460. Thus, the correct answer is C.

Example 2: 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.

A. Rs.1900                 B. Rs. 2660                       C. Rs. 2800                D. Rs. 2840

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. 7030×1437=Rs. 2660