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
Difficult problems:
1.P and Q started a business investing Rs 85,000 and Rs 15,000respectively. 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
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
Difficult problems:
1.P and Q started a business investing Rs 85,000 and Rs 15,000respectively. 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
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