Partnership

Important Facts: 

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:

1.When the investments of all the partners are do 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*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

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

Formulae

1.When investments of A and B are Rs x and Rs y 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 A invests Rs x for p months and B invests Rs y for q months,
then A's share profit:B's share of profit=xp:yq

Short cuts:

1.In case of 3 A,B,C investments then individual share is to be found 
then A=16000 , B=32,000 , C=40,000

Sol: A:B:C=16:32:40
          =2:4:5`
then individual share can be easily known.

2.If business mans A contributes for 5 months and B contributes for 9 
months then share of B in the total profit of Rs 26,8000 ,A = Rs 15000,
B =Rs 12000 

Sol: 15000*5 : 12000*9
          25 : 36
    for 36 parts=268000*(36/61)
                =Rs 158.16 
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Difficult problems:

1.P and Q started a business investing Rs 85,000 and Rs 15,000 
respectively. In what ratio the profit earned after 2 years be divided
between P and Q respectively?

Sol:  85,000*2 : 15,000*2
          17*2 : 3*2=34:6

2.A,B and C started a business by investing Rs 1,20,000, Rs 1,35,000 
and Rs 1,50,000.Find the share of each ,out of an annual profit of
Rs 56,700?

Sol: Ratio of shares of A,B and C=Ratio of their investments
           120,000:135,000:150,000
	   =8:9:10
   A's share=Rs 56,700*(8/27)=Rs 16,800
   B's share =Rs 56,700*(9/27)=Rs 18,900
   C's share =Rs 56,700*(10/27)=Rs 21,000

3.3 milkman A,B,C rented a pasture A grazed his 45 cows for 12 days 
B grazed his 36 cows for 15 days and c 60 cows for 10 days.If b's 
share of rent was Rs 540 What is the total rent?

Sol:      45*12:36*15:60*10
             =9:9:10
      9 parts is equal to Rs 540
    then one part is equal to Rs 60
         total rent=60*28=Rs 1680

4.Ramu and Krishna entered into a partnership with Rs 50,000 and 
Rs 60,000, after 4 months Ramu invested Rs 25,000 more while Krishna
withdraw Rs 20,000 . Find the share of Ramu in the annual profit of
Rs 289,000.

Sol: Ramu : Krishna=50,000*4+75,000*8:60,000*4+40,000*8
                =10:7
    Ramu's annual profit=289000*(10/17)=Rs 170,000

5.A,B,C enter into partnership .A invests 3 times as much as B invests 
and B invests two third of what C invests. At the end of the year ,the 
profit earned is Rs 6600. what is the share of B?

Sol:          let C's capital =Rs x
            B's capital=Rs (2/3)*x
	  A's capital =3*(2/3)*x=Rs 2x
      ratio of their capitals=2x:(2/3)*x:x
                            =6x:2x;3x
	B's share =Rs 6600(2/11)=Rs 1200
	
6.A,B and C enter into a partnership by investing in the ratio of 3:2:4.
After one year ,B invests another Rs 2,70,000 and C,at the end of 2 
years, also invests Rs 2,70,000.At the end of 3 years ,profit are shared
in the ratio of 3:4:5.Find the initial investment of each?

Sol: Initial investments of A,B,c be Rs 3x, Rs 2x, Rs 4x then for 3 years 
      (3x*36):[(2x*12)+(2x+270000)*24]:[(4x*24)+(4x+270000)*12]=3:4:5
         108x:(72x+640,000):(144x+3240000)=3:4:5
         108x:72x+6480000:144x+3240000=3:4:5
             (108x)/(72x+6480000)=3/4
               432x=216x+19440000
                  216x=19440000
                     x=Rs 90000
     A's initial investment=3x=3*90,000=Rs 2,70,000
     B's initial investment=2x=2*90,000=Rs 1,80,000
     C's initial investment=4x=4*90,000=Rs 3,60,000