business mathematics

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.

Formula:

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

Partnership problems

Partnership problems

Little 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