Partnership

Partnership: 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.
(ii) When investments are for different time, 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.

Working & 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.

Solved Problems

Ex. 1. Manoj and Vinod Started a business by investing Rs. 120000 and Rs. 135000 respectively. Find the share of each, out of an annual profit of Rs.35700

Sol. Ratio of their shares = 120000 : 135000 = 8: 9
:. Man oj' s share = Rs. [35700 x ]= Rs. 16800.
Vinod's sharee = Rs.[35700 x ]= Rs. 18900.

Ex. 2. Sanjeev started a business by investing Rs. 36000. After 3 months Rajeev joined him by investing Rs. 36000. Out of an annual profit of Rs. 37100, find the share of each.

Sol. Ratio of their capitals = 36000 x 12 : 36000 x 9 = 4: 3.
Sanjeev's share = Rs. (37100 x )= Rs. 21200.
Rajeev's share = Rs. (37100 x )= Rs. 15900.

Ex. 3. A, Band C start a business each investing Rs. 20000. After 5 months A withdrew Rs. 5000, B withdrew Rs. 4000 and C invests Rs. 6000 more. At the end of the year, a total profit of Rs. 69900 was recorded. Find the sharere of each.

Sol. Ratio of the capitals of A, B and C.
=( 20000 x 5 + 15000 x 7) : (20000 x5 + 16000 x7) :(20000 x 5 + 26000 x 7)
= 205000 : 212000 : 282000 = 205 : 212 : 282
A’s Share = Rs. = Rs. 20500,
B's share = Rs. = Rs. 21200,
C's share = Rs. = Rs. 28200.

Ex. 4. A stlIrted a business with Rs. 21000 and is joined afterwards by B with Rs. 36000. After how many months did B join, if the profits at the end of the year are divided equally?

Sol. Suppose B joined after x months.
        Then, B's money was invested for (12 - x) months.
         :. 21000 x 12 = 36000 x (12 - x) 36x = 180 x = 5.
        So, B joined after 5 months. .

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