Formulas
Simple Partnership:
$\dfrac{Capital\:of \:A}{Capital \:of \:B}=\dfrac{Profit\:of \:A}{Profit\: of \:B}$
Capital of A : Capital of B = Profit of A : Profit of B
Compound Partnership:
$\dfrac{Capital\:of \:A\times Time\: Period \:of \:A}{Capital \:of \:B\times Time \:Period \:of \:B}=\dfrac{Profit\:of \:A}{Profit\: of \:B}$
Capital of A × Time period of A : Capital of B × Time period of B = Profit of A : Profit of B
If n partners are investing for different period of time then
C1T1 : C2T2 : C3T3 : … : CnTn = P1 : P2 : P3 : … : Pn
Where C is the capital invested, T is time period of capital invested and P is profit earned.
Partnership:
When more than one person agree to invest their money to run a business or firm then this kind of agreement is called partnership. The persons involved in the partnership are called partners.
Two types of partnership.
- Simple Partnership
- Compound Partnership
Simple Partnership:
If two partners A and B are investing their money to run a business,capitals of partners are invested for the same period of time.
$\dfrac{Capital\:of \:A}{Capital \:of \:B}=\dfrac{Profit\:of \:A}{Profit\: of \:B}$
Capital of A : Capital of B = Profit of A : Profit of B
Example:
P and Q invested in a business. The profit earned was divided in the ratio 2 : 3. If P invested Rs 40000, then find the amount invested by Q?
Let the amount invested by Q = q
40000:Q=2:3
40000×3=2Q
$Q=\dfrac{40000\times3}{2}$
Q=60000
Exercise:
Here A's and B's capitals are there for equal time. Hence
A : B = 85000 : 15000
= 85 : 15
= 17 : 3
Compound Partnership:
If two partners A and B are investing their money for different period of time to run a business, capitals of partners are invested for the different period of time.
$\dfrac{Capital\:of \:A\times Time\: Period \:of \:A}{Capital \:of \:B\times Time \:Period \:of \:B}=\dfrac{Profit\:of \:A}{Profit\: of \:B}$
Capital of A × Time period of A : Capital of B × Time period of B = Profit of A : Profit of B
Example:
Jack and Jill start a business by investing 2,000 for 8 months and 3,000 for 6 months respectively. If their total profit is 510 and then what is profit of Jill?
Capital of Jack = 2000 and Time period = 8 months
Capital of Jill = 3000 and Time period = 6 months
$\dfrac{Capital\:of \:Jack\times Time\: Period \:of \:Jack}{Capital \:of \:Jill\times Time \:Period \:of \:Jill}=\dfrac{Profit\:of \:Jack}{Profit\: of \:Jill}$
$\dfrac{2000\times 8}{3000\times 6 }=\dfrac{Profit\:of \:Jack}{Profit\: of \:Jill}$
So, Profit of Jack : Profit of Jill = 8 : 9
So we have 8 + 9 = 17 parts of total profit.
Out of this 17 parts, Jack will get 8 parts and Jill will get 9 parts.
Now, total profit is 510
So, One Part = 510/17 = 30.
Jill’s profit = 30 × 9 = 270 and
Jack’s profit = 30 × 8 = 240.
Exercise:
Let B joined for X months. Then
85000×12:42500×X=3:1
850×12:425X=3:1
850×12×1=3×425X
850×4=425X
X=8
If n partners are investing for different period of time then
C1T1 : C2T2 : C3T3 : … : CnTn = P1 : P2 : P3 : … : Pn
Where C is the capital invested, T is time period of capital invested and P is profit earned.
Example:
Raju, Kamal and Vinod start a business by investing Rs 5,000 for 12 months, Rs 8,000 for 9 months and Rs 10,000 for 6 months. If at the end of the year their total profit is Rs 2000 then find the profit of each partner?
Raju’s investment is 5000 for 12 months.
Kamal’s investment is 8000 for 9 months.
Vinod’s investment is 10000 for 6 months.
So their ratio of investments is
5000 × 12 : 8000 × 9 : 10000 × 6
60 : 72 : 60
5 : 6 : 5
So their profit,
Raju : Kamal : Vinod = 5 : 6 : 5
So there are 5 + 6 + 5 = 16 parts of profit.
Out of these 16 parts, Raju will get 5 parts, Kamal will get 6 parts and Vinod will get 5 parts.
So, Total profit = 2000
Raju’s profit =$\dfrac{5}{16} \times 2000$ = 625
Kamal’s profit = $\dfrac{6}{16} \times 2000$ = 750
Vinod’s profit = $\dfrac{5}{16} \times 2000$ = 625
Exercise:
=6000*5:3600*6:7500*3
=60*5 : 36*6 : 75*3
=100: 72: 75
So there are 100 + 72 + 75 = 247 parts of profit.
Out of these 247 parts, A will get 100 parts, B will get 72 parts and C will get 75 parts.
Total profit = 7410
Share of A=$\dfrac{100}{247}\times 7410 $= 3000
Two types of partners
- Sleeping Partner
- Working Partner
Sleeping Partner:
Sleeping partner is the person who provides only investment but does not take part in running the business.
Working Partner:
Working partner is the person who not only invests the money but also takes part in running the business. For this work he is paid some salary or some percent of profit in addition.
Example:
Raju and Ramu enter into partnership,investing Rs.3000 and Rs.2000 respectively.Raju was the sleeping partner.At the end of the month,both got Rs.150 each.What was Ramu's remuneration for his work?
Raju,Ramu's investments 3000,2000
Profit Ratio=3:2
Raju 3 parts=Rs.150
Ramu has to be get 2 parts=Rs.100
So Ramu get additional (150-100)=Rs.50 as remuneration.
Exercise:
A's investment:B's investment
15000:25000
15:25
3:5
So there are 3+5 = 8 parts of profit.
Total Profit=9600
A receives 10% of the profit
9600*10/100 = 960
Total Profit-A's 10% profit
9600 - 960 = 8640
So,
A's Share
=8640*3/8
= 3240
Therefore Total Amout Received by A is
= 3240 + 960
= 4200